Advanced search
Publication Cover
Communications in Algebra Volume 29, 2001 - Issue 5
Submit an article Journal homepage
222
Views
86
CrossRef citations to date
0
Altmetric
Original Articles

ON 2-PRIMAL ORE EXTENSIONS

Greg Marks Department of Mathematics & Mathematical Computer Science, St. Louis University, St. Louis, Missouri, 63103, U.S.A.
Pages 2113-2123 | Received 01 Nov 1999, Published online: 19 Aug 2006

Citations (86)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (19)

Sebastián Higuera & Armando Reyes. (2023) On weak annihilators and nilpotent associated primes of skew PBW extensions. Communications in Algebra 51:11, pages 4839-4861.
Read now
Juncheol Han, Chang Ik Lee & Yang Lee. (2023) Symmetry on zero and idempotents. Communications in Algebra 51:2, pages 464-474.
Read now
Héctor Suárez, Andrés Chacón & Armando Reyes. (2022) On NI and NJ skew PBW extensions. Communications in Algebra 50:8, pages 3261-3275.
Read now
Xavier Mary. (2022) N-chained semigroups and -perspective modules and rings. Communications in Algebra 50:1, pages 163-181.
Read now
Henry Chimal-Dzul, Sergio López-Permouth & Steve Szabo. (2021) Characterizations of certain Morita context rings. Communications in Algebra 49:8, pages 3409-3422.
Read now
Juncheol Han, Yang Lee & Sangwon Park. (2021) Structure of NI rings related to centers. Communications in Algebra 49:2, pages 621-630.
Read now
Kamal Paykan & Ahmad Moussavi. (2020) Some characterizations of 2-primal skew generalized power series rings. Communications in Algebra 48:6, pages 2346-2357.
Read now
Steve Szabo. (2019) Some minimal rings related to 2-primal rings. Communications in Algebra 47:3, pages 1287-1298.
Read now
Kwang Jin Choi, Tai Keun Kwak & Yang Lee. (2018) Rings whose nilpotents form a multiplicative set. Communications in Algebra 46:8, pages 3229-3240.
Read now
Sushma Singh & Om Prakash. (2018) A note on lower nil M-Armendariz rings. Cogent Mathematics & Statistics 5:1.
Read now
Abdullah M. Abdul-Jabbar, Chenar Abdul Kareem Ahmed, Tai Keun Kwak, Yang Lee & Young Joo Seo. (2017) Zero commutativity of nilpotent elements skewed by ring endomorphisms. Communications in Algebra 45:11, pages 4881-4895.
Read now
Abdullah M. Abdul-Jabbar, Chenar Abdul Kareem Ahmed, Tai Keun Kwak & Yang Lee. (2017) Reflexivity with maximal ideal axes. Communications in Algebra 45:10, pages 4348-4361.
Read now
A. R. Nasr-Isfahani. (2016) Radicals of Ore Extension of Skew Armendariz Rings. Communications in Algebra 44:3, pages 1302-1320.
Read now
A.R. Nasr-Isfahani. (2015) On NI Skew Polynomial Rings. Communications in Algebra 43:12, pages 5113-5120.
Read now
Tai Keun Kwak, Min Jung Lee & Yang Lee. (2014) On Sums of Coefficients of Products of Polynomials. Communications in Algebra 42:9, pages 4033-4046.
Read now
Tai Keun Kwak & Yang Lee. (2012) Reflexive Property of Rings. Communications in Algebra 40:4, pages 1576-1594.
Read now
Alireza Nasr-Isfahani & Ahmad Moussavi. (2011) On Skew Power Serieswise Armendariz Rings. Communications in Algebra 39:9, pages 3114-3132.
Read now
Guoyin Zhang, Fanggui Wang & Wenbin Xu. (2007) Gelfand Factor Rings and Weak Zariski Topologies. Communications in Algebra 35:8, pages 2628-2645.
Read now
C. Y. Hong, H. K. Kim, N. K. Kim, T. K. Kwak, Y. Lee & K. S. Park. (2007) Rings Whose Nilpotent Elements form a Levitzki Radical Ring. Communications in Algebra 35:4, pages 1379-1390.
Read now

Articles from other publishers (67)

Héctor Suárez & Armando Reyes. (2023) $$\Sigma$$-Semicommutative rings and their skew PBW extensions. São Paulo Journal of Mathematical Sciences 17:2, pages 531-554.
Crossref
Hongying Chen, Juan Huang, Tai Keun Kwak & Yang Lee. (2022) On the condition that powers preserve noncentralness. Journal of Algebra and Its Applications 22:11.
Crossref
Steve Szabo. (2023) A Taxonomy of Dedekind-Finite and Reflexive Rings. Mediterranean Journal of Mathematics 20:5.
Crossref
Sera Kim, Tai Keun Kwak, Chang Ik Lee, Yang Lee & Sang Jo Yun. (2022) Reflexive ideals and reflexively closed subsets in rings. Journal of Algebra and Its Applications 22:05.
Crossref
Ruhollah Barati & Ahmad Moussavi. (2023) A Note on Weakly Nil-Clean Rings. Mediterranean Journal of Mathematics 20:2.
Crossref
Guanglin Ma & Yao Wang. (2022) On weak zero-clean rings. International Journal of Algebra and Computation 32:08, pages 1459-1476.
Crossref
Abdullah Harmanci, Yosum Kurtulmaz & Burcu Ungor. (2022) Rings which are duo on Zhou radical. São Paulo Journal of Mathematical Sciences 16:2, pages 871-892.
Crossref
H. Chimal-Dzul & S. Szabo. (2021) Classification of nonsemicommutative rings. Acta Mathematica Hungarica 165:1, pages 48-62.
Crossref
Vahid Nourozi, Farhad Rahmati & Morteza Ahmadi. (2020) McCoy property of Hurwitz series rings. Asian-European Journal of Mathematics 14:06, pages 2150105.
Crossref
Chan Yong HONG, Hong Kee KİM, Nam Kyun KİM, Tai Keun KWAK & Yang LEE. (2020) One-sided duo property on nilpotents. Hacettepe Journal of Mathematics and Statistics 49:6, pages 1974-1987.
Crossref
Om Prakash, Sushma Singh & K.P. Shum. (2020) On Almost Armendariz Ring. Algebra Colloquium 27:02, pages 199-212.
Crossref
Arnab Bhattacharjee. (2018) Reflexive-nilpotents-property skewed by ring endomorphisms. Arabian Journal of Mathematics 9:1, pages 63-72.
Crossref
A. Niño & A. Reyes. (2020) Some remarks about minimal prime ideals of skew Poincaré-Birkhoff-Witt extensions. Algebra and Discrete Mathematics 30:2, pages 207-229.
Crossref
Arnab Bhattacharjee & Uday Shankar Chakraborty. (2019) Reflexive property on rings with involution. Asian-European Journal of Mathematics 12:07, pages 2050011.
Crossref
Abdolreza Tehranchi & Kamal Paykan. (2019) A characterization of 2-primal and NI rings over skew inverse Laurent series rings. Journal of Algebra and Its Applications 18:12, pages 1950221.
Crossref
Abdolreza Tehranchi & Kamal Paykan. (2018) Some results on skew Hurwitz series rings. Rendiconti del Circolo Matematico di Palermo Series 2 68:2, pages 329-337.
Crossref
Orest D. Artemovych. (2019) Associative rings in which nilpotents form an ideal. Studia Scientiarum Mathematicarum Hungarica 56:2, pages 177-184.
Crossref
Tugce Pekacar Calci, Abdullah Harmanci & Burcu Ungor. (2016) An approach to quasipolarity for rings along nilpotent elements. Boletín de la Sociedad Matemática Mexicana 24:1, pages 95-106.
Crossref
Kamal Paykan & Ahmad Moussavi. (2017) Study of skew inverse Laurent series rings. Journal of Algebra and Its Applications 16:12, pages 1750221.
Crossref
Kamal Paykan & Ahmad Moussavi. (2017) McCoy property and nilpotent elements of skew generalized power series rings. Journal of Algebra and Its Applications 16:10, pages 1750183.
Crossref
Masoud Azimi & Ahmad Moussavi. (2017) On nilpotent elements of ore extensions. Asian-European Journal of Mathematics 10:03, pages 1750043.
Crossref
Abdollah Alhevaz, Ebrahim Hashemi & Michał Ziembowski. (2016) Nilradicals of the unique product monoid rings. Journal of Algebra and Its Applications 16:07, pages 1750133.
Crossref
Kamal Paykan & Ahmad Moussavi. (2016) Nilpotent elements and nil-Armendariz property of skew generalized power series rings. Asian-European Journal of Mathematics 10:02, pages 1750034.
Crossref
Mehdi Kheradmand, Hossain Khabazian, Tai Keun Kwak & Yang Lee. (2017) Reflexive property restricted to nilpotents. Journal of Algebra and Its Applications 16:03, pages 1750044.
Crossref
Mehdi Kheradmand, Hong Kee Kim, Tai Keun Kwak & Yang Lee. (2017) Reflexive property on nil ideals. Journal of Algebra and Its Applications 16:02, pages 1750022.
Crossref
Kamal Paykan. (2016) Nilpotent elements of skew Hurwitz series rings. Rendiconti del Circolo Matematico di Palermo (1952 -) 65:3, pages 451-458.
Crossref
Abdollah Alhevaz & Ebrahim Hashemi. (2016) An Alternative Perspective on Skew Generalized Power Series Rings. Mediterranean Journal of Mathematics 13:6, pages 4723-4744.
Crossref
Chan Yong Hong, Nam Kyun Kim & Yang Lee. (2016) On LN rings and topological properties of prime spectra. Journal of Algebra and Its Applications 15:06, pages 1650102.
Crossref
Yao Wang, Meimei Jiang & Yanli Ren. (2016) π-Armendariz rings relative to a monoid. Frontiers of Mathematics in China 11:4, pages 1017-1036.
Crossref
Nam Kyun Kim, Tai Keun Kwak & Yang Lee. (2016) ON A GENERALIZATION OF RIGHT DUO RINGS. Bulletin of the Korean Mathematical Society 53:3, pages 925-942.
Crossref
Juncheol Han, Yui-Yun Jung, Yang Lee & Hyo Jin Sung. (2014) INSERTION-OF-FACTORS-PROPERTY WITH FACTORS NILPOTENTS. Korean Journal of Mathematics 22:4, pages 611-619.
Crossref
Nam Kyun Kim, Tai Keun Kwak & Yang Lee. (2014) SEMICOMMUTATIVE PROPERTY ON NILPOTENT PRODUCTS. Journal of the Korean Mathematical Society 51:6, pages 1251-1267.
Crossref
L. Márki & S. Tumurbat. (2014) On Radicals of Polynomial Rings. Acta Mathematica Hungarica 144:1, pages 227-235.
Crossref
Yueming Xiang & Lunqun Ouyang. (2014) Rings Whose Simple Singular Modules are PS-Injective. Kyungpook mathematical journal 54:3, pages 471-476.
Crossref
Da Woon Jung, Yang Lee & Hyo Jin Sung. (2014) REVERSIBILITY OVER PRIME RADICALS. Korean Journal of Mathematics 22:2, pages 279-288.
Crossref
A. R. NASR-ISFAHANI. (2013) ORE EXTENSIONS OF 2-PRIMAL RINGS. Journal of Algebra and Its Applications 13:03, pages 1350117.
Crossref
Tai Keun Kwak & Yang Lee. (2013) REFLEXIVE PROPERTY ON IDEMPOTENTS. Bulletin of the Korean Mathematical Society 50:6, pages 1957-1972.
Crossref
P. Dheena & C. Jenila. (2013) TOPOLOGICAL CONDITIONS OF NI NEAR-RINGS. Communications of the Korean Mathematical Society 28:4, pages 669-677.
Crossref
Juncheol Han, Hong Kee Kim & Yang Lee. (2013) ARMENDARIZ PROPERTY OVER PRIME RADICALS. Journal of the Korean Mathematical Society 50:5, pages 973-989.
Crossref
Victor Camillo, Tai Keun Kwak & Yang Lee. (2013) ON A GENERALIZATION OF MCCOY RINGS. Journal of the Korean Mathematical Society 50:5, pages 959-972.
Crossref
MOHAMMAD HABIBI & RAOUFEH MANAVIYAT. (2013) A GENERALIZATION OF NIL-ARMENDARIZ RINGS. Journal of Algebra and Its Applications 12:06, pages 1350001.
Crossref
NICO J. GROENEWALD & DAVID SSEVVIIRI. (2013) 2-PRIMAL MODULES. Journal of Algebra and Its Applications 12:05, pages 1250226.
Crossref
Tai Keun Kwak & Yang Lee. (2013) ON NILPOTENT POWER SERIES WITH NILPOTENT COEFFICIENTS. Korean Journal of Mathematics 21:1, pages 41-53.
Crossref
R. M. Salem, A. M. Hassanein & M. A. Farahat. (2013) MAL'CEV–NEUMANN SERIES OVER ZIP AND WEAK ZIP RINGS. Asian-European Journal of Mathematics 05:04, pages 1250058.
Crossref
DA WOON JUNG, NAM KYUN KIM, YANG LEE & SUNG PIL YANG. (2012) NIL-ARMENDARIZ RINGS AND UPPER NILRADICALS. International Journal of Algebra and Computation 22:06, pages 1250059.
Crossref
M. HABIBI & A. MOUSSAVI. (2012) NILPOTENT ELEMENTS AND NIL-ARMENDARIZ PROPERTY OF MONOID RINGS. Journal of Algebra and Its Applications 11:04, pages 1250080.
Crossref
A. R. NASR-ISFAHANI & A. MOUSSAVI. (2012) A GENERALIZATION OF REDUCED RINGS. Journal of Algebra and Its Applications 11:04, pages 1250070.
Crossref
Lunqun Ouyang. (2012) SPECIAL WEAK PROPERTIES OF GENERALIZED POWER SERIES RINGS. Journal of the Korean Mathematical Society 49:4, pages 687-701.
Crossref
M. Habibi & A. Moussavi. (2012) ON NIL SKEW ARMENDARIZ RINGS. Asian-European Journal of Mathematics 05:02, pages 1250017.
Crossref
Jin-Eon Baek, Woo-Young Chin, Ji-Woong Choi, Tae-Hyun Eom, Young-Cheol Jeon & Yang Lee. (2012) INSERTION-OF-FACTORS-PROPERTY ON NILPOTENT ELEMENTS. Bulletin of the Korean Mathematical Society 49:2, pages 381-394.
Crossref
Najat M. Muthana & S. Khalid Nauman. (2012) On Commutativity of Semiprime Right Goldie C<i><sub>k</sub></i>-Rings. Advances in Pure Mathematics 02:04, pages 217-219.
Crossref
TAI KEUN KWAK & YANG LEE. (2011) RINGS OVER WHICH COEFFICIENTS OF NILPOTENT POLYNOMIALS ARE NILPOTENT. International Journal of Algebra and Computation 21:05, pages 745-762.
Crossref
Young Chun, Young-Cheol Jeon, Sung-Kyung Kang, Key-Nyoung Lee & Yang Lee. (2011) A CONCEPT UNIFYING THE ARMENDARIZ AND NI CONDITIONS. Bulletin of the Korean Mathematical Society 48:1, pages 115-127.
Crossref
Jin-Mun Jeong, Eun-Young Ju & Yong-Han Kang. (2011) APPROXIMATE CONTROLLABILITY FOR DIFFERENTIAL EQUATIONS WITH QUASI-AUTONOMOUS OPERATORS. Bulletin of the Korean Mathematical Society 48:1, pages 1-8.
Crossref
Young-Cheol Jeon, Yang Lee & Sung-Ju Ryu. (2010) A STRUCTURE ON COEFFICIENTS OF NILPOTENT POLYNOMIALS. Journal of the Korean Mathematical Society 47:4, pages 719-733.
Crossref
Chan Huh, Chang Ik Lee & Yang Lee. (2012) On Rings Whose Strongly Prime Ideals Are Completely Prime. Algebra Colloquium 17:02, pages 283-294.
Crossref
Chan-Yong Hong, Nam-Kyun Kim & Tai-Keun Kwak. (2010) ON QUASI-RIGID IDEALS AND RINGS. Bulletin of the Korean Mathematical Society 47:2, pages 385-399.
Crossref
Hong-Kee Kim, Nam-Kyun Kim, Mun-Seob Jeong, Yang Lee, Sung-Ju Ryu & Dong-Eun Yeo. (2009) ON CONDITIONS PROVIDED BY NILRADICALS. Journal of the Korean Mathematical Society 46:5, pages 1027-1040.
Crossref
SEO UN HWANG, NAM KYUN KIM & YANG LEE. (2009) ON RINGS WHOSE RIGHT ANNIHILATORS ARE BOUNDED. Glasgow Mathematical Journal 51:3, pages 539-559.
Crossref
Kyung-Yuen Ham, Young-Cheol Jeon, Jin-Woo Kang, Nam-Kyun Kim, Won-Jae Lee, Yang Lee, Sung-Ju Ryu & Hae-Hun Yang. (2008) IFP RINGS AND NEAR-IFP RINGS. Journal of the Korean Mathematical Society 45:3, pages 727-740.
Crossref
Seo-Un Hwang, Yang Lee & Kwang-Sug Park. (2007) ON STRONGLY 2-PRIMAL RINGS. Honam Mathematical Journal 29:4, pages 555-567.
Crossref
Chan Huh, Chang-Ik Lee, Kwang-Sug Park & Sung-Ju Ryu. (2007) ON II-ARMENDARIZ RINGS. Bulletin of the Korean Mathematical Society 44:4, pages 641-649.
Crossref
Seo-Un Hwang, Young-Cheol Jeon & Kwang-Sug Park. (2007) ON NCI RINGS. Bulletin of the Korean Mathematical Society 44:2, pages 215-223.
Crossref
Chan Yong Hong, Young Cheol Jeon, Kyoung Hwan Kim, Nam Kyun Kim & Yang Lee. (2006) Weakly regular rings with ACC on annihilators and maximality of strongly prime ideals of weakly regular rings. Journal of Pure and Applied Algebra 207:3, pages 565-574.
Crossref
Yong Uk Cho, Nam Kyun Kim, Mi Hyang Kwon & Yang Lee. (2012) Classical Quotient Rings and Ordinary Extensions of 2-Primal Rings. Algebra Colloquium 13:03, pages 513-523.
Crossref
Seo Un Hwang, Young Cheol Jeon & Yang Lee. (2006) Structure and topological conditions of NI rings. Journal of Algebra 302:1, pages 186-199.
Crossref
Greg Marks. (2003) A taxonomy of 2-primal rings. Journal of Algebra 266:2, pages 494-520.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.