Advanced search
Publication Cover
Communications in Algebra Volume 36, 2008 - Issue 2
Submit an article Journal homepage
711
Views
56
CrossRef citations to date
0
Altmetric
Original Articles

Generalizations of Prime Ideals

D. D. Anderson Department of Mathematics, The University of Iowa, Iowa City, Iowa, USACorrespondence[email protected]
&
Malik Bataineh Department of Mathematics, The University of Iowa, Iowa City, Iowa, USAView further author information
Pages 686-696 | Received 28 Sep 2006, Published online: 07 Apr 2008

Citations (56)

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 (8)

Emel Aslankarayigit Ugurlu. (2021) Generalizations of r-ideals of commutative rings. Journal of Interdisciplinary Mathematics 24:8, pages 2283-2293.
Read now
Suat Koç. (2021) On weakly 2-prime ideals in commutative rings. Communications in Algebra 49:8, pages 3387-3397.
Read now
Rachida El Khalfaoui & Najib Mahdou. (2020) The ϕ-Krull dimension of some commutative extensions. Communications in Algebra 48:9, pages 3800-3810.
Read now
P. Yiarayong & M. . (2018) On generalizations of classical primary submodules over commutative rings. Cogent Mathematics & Statistics 5:1.
Read now
Sina Hedayat & Esmaeil Rostami. (2017) Decomposition of ideals into pseudo-irreducible ideals. Communications in Algebra 45:4, pages 1711-1718.
Read now
M. Ebrahimpour. (2014) On Generalizations of Prime Ideals (II). Communications in Algebra 42:9, pages 3861-3875.
Read now
M. Ebrahimpour & R. Nekooei. (2012) On Generalizations of Prime Ideals. Communications in Algebra 40:4, pages 1268-1279.
Read now
DavidF. Anderson & Ayman Badawi. (2011) On n-Absorbing Ideals of Commutative Rings. Communications in Algebra 39:5, pages 1646-1672.
Read now

Articles from other publishers (48)

Rabia Nagehan Üregen. (2024) A Note On φ- Strongly Quasi Primary Ideals. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi 17:1, pages 301-307.
Crossref
Ameer Jaber. (2024) On ϕ-S-1-absorbing δ-primary superideals over commutative super-rings. Asian-European Journal of Mathematics 17:02.
Crossref
Mohamed CHHİTİ, Bayram Ali ERSOY, Khalid KAIBA & Ünsal TEKİR. (2023) $\delta (0)$-Ideals of Commutative Rings. International Electronic Journal of Algebra.
Crossref
Mohammed Hamoda & Mohammed Issoual. (2023) On weakly (m, n)−closed δ−primary ideals of commutative rings. Proyecciones (Antofagasta) 42:5, pages 1289-1306.
Crossref
Hani KHASHAN & Ece YETKİN ÇELİKEL. (2023) S-n-ideals of commutative rings. Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 72:1, pages 199-215.
Crossref
Moussa Thiaw. 2023. Recent Advances in Fuzzy Sets Theory, Fractional Calculus, Dynamic Systems and Optimization. Recent Advances in Fuzzy Sets Theory, Fractional Calculus, Dynamic Systems and Optimization 326 331 .
Ahmad Yousefian Darani, Najib Mahdou & Sanae Moussaoui. (2021) Strongly ϕ-n-irreducible ideals. Journal of Algebra and Its Applications 21:12.
Crossref
Hao Guan, Elif Kaya, Melis Bolat, Serkan Onar, Bayram Ali Ersoy & Kostaq Hila. (2022) - -Primary Hyperideals in Krasner Hyperrings . Mathematical Problems in Engineering 2022, pages 1-12.
Crossref
Peng Xu, Melis Bolat, Elif Kaya, Serkan Onar, Bayram Ali Ersoy & Kostaq Hila. (2022) -Hyperideals and Generalizations of -Hyperideals in Krasner Hyperrings . Mathematical Problems in Engineering 2022, pages 1-10.
Crossref
Esmaeil Rostami. (2021) On S-pseudo-irreducible ideals. Journal of Algebra and Its Applications 21:07.
Crossref
F. Farzalipour & P. Ghiasvand. (2021) Graded φ-2-absorbing hyperideals in graded multiplicative hyperrings. Asian-European Journal of Mathematics 15:06.
Crossref
Bayram Ali Ersoy, Ünsal Tekir, Elif Kaya, Melis Bolat & Suat Koç. (2022) On $$\phi$$-$$\delta$$-Primary Submodules. Iranian Journal of Science and Technology, Transactions A: Science 46:2, pages 421-427.
Crossref
Esmaeil Rostami, Sina Hedayat, Reza Nekooei & Somayeh Karimzadeh. (2020) Comaximal factorization of lifting ideals. Journal of Algebra and Its Applications 21:03.
Crossref
Emel Aslankarayiğit Uğurlu, Suat Koç & Ünsal Tekir. (2021) Generalization of 2-absorbing quasi primary ideals. Novi Sad Journal of Mathematics 52:1, pages 155-171.
Crossref
J. Catherine Grace John. 2022. Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy. Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy 3 11 .
Ortaç ÖNEŞ. (2021) On Prime Ideals Related to an Ideal in a Commutative Ring. Gazi University Journal of Science Part A: Engineering and Innovation 8:4, pages 451-458.
Crossref
Wala’a Alkasasbeh & Malik Bataineh. (2021) Generalizations of S- Prime Ideals. WSEAS TRANSACTIONS ON MATHEMATICS 20, pages 694-699.
Crossref
Eda Yildiz, Unsal Tekir & Suat Koc. (2021) On $$\phi $$-1-absorbing prime ideals. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 62:4, pages 907-918.
Crossref
I G A W Wardhana, N D H Nghiem, N W Switrayni & Q Aini. (2021) A note on almost prime submodule of CSM module over principal ideal domain. Journal of Physics: Conference Series 2106:1, pages 012011.
Crossref
Pairote Yiarayong. (2021) On generalizations of quasi-prime ideals of an ordered left almost semigroups. Afrika Matematika 32:5-6, pages 969-982.
Crossref
M. Ebrahimpour. (2020) Some results about ϕ-primal subsemimodules. Journal of Algebra and Its Applications 20:06, pages 2150093.
Crossref
Haider A. Ramadhan & Nuhad S. Al. Mothafar. (2021) On Small Semiprime Submodules. Journal of Physics: Conference Series 1818:1, pages 012142.
Crossref
Hani A. KHASHAN & Amal B. BANI-ATA. (2021) J-IDEALS OF COMMUTATIVE RINGS. International Electronic Journal of Algebra 29:29, pages 148-164.
Crossref
Ayten Pekin, Ünsal Tekir & Özge Kılıç. (2020) S-Semiprime Submodules and -Reduced Modules . Journal of Mathematics 2020, pages 1-7.
Crossref
F. Farshadifar & H. Ansari-Toroghy. (2020) $$\psi $$-Second submodules of a module. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 61:3, pages 571-578.
Crossref
Ameer Jaber. (2018) Properties of ϕ-δ-primary and 2-absorbing δ-primary ideals of commutative rings. Asian-European Journal of Mathematics 13:01, pages 2050026.
Crossref
Ece YETKİN ÇELİKEL. (2019) Generalizations of n-ideals of Commutative RingsDeğişmeli Halkalarda n-ideallerin Genelleştirmeleri. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi 12:2, pages 650-657.
Crossref
P. Karimi Beiranvand & R. Beyranvand. (2019) Almost prime and weakly prime submodules. Journal of Algebra and Its Applications 18:07, pages 1950129.
Crossref
Malik Bataineh & Akram Al-Areqie. (2019) On almost fuzzy prime ideals and sub-modules. Afrika Matematika 30:3-4, pages 611-621.
Crossref
M. K. Dubey & P. Aggarwal. (2018) On 2-Absorbing Ideals in Commutative Rings with Unity. Lobachevskii Journal of Mathematics 39:2, pages 185-190.
Crossref
Seçil Çeken & Mustafa Alkan. On strongly 2-absorbing second submodules. On strongly 2-absorbing second submodules.
Razieh Moradi & Mahdieh Ebrahimpour. (2016) On ϕ-2-Absorbing Primary Submodules. Acta Mathematica Vietnamica 42:1, pages 27-35.
Crossref
Ameer Jaber. (2017) Properties of -Primal Graded Ideals . Journal of Mathematics 2017, pages 1-8.
Crossref
David F. Anderson & Ayman Badawi. (2017) On (m,n)-closed ideals of commutative rings. Journal of Algebra and Its Applications 16:01, pages 1750013.
Crossref
Ayman Badawi. 2017. Rings, Polynomials, and Modules. Rings, Polynomials, and Modules 33 52 .
Hosein Fazaeli Moghimi & Sadegh Rahimi Naghani. (2016) ON n-ABSORBING IDEALS AND THE n-KRULL DIMENSION OF A COMMUTATIVE RING. Journal of the Korean Mathematical Society 53:6, pages 1225-1236.
Crossref
Hojjat Mostafanasab & Ahmad Yousefian Darani. (2016) ON 𝜙-n-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS. Journal of the Korean Mathematical Society 53:3, pages 549-582.
Crossref
Unsal Tekir, Suat Koç, Kursat Hakan Oral & Kar Ping Shum. (2015) On 2-Absorbing Quasi-Primary Ideals in Commutative Rings. Communications in Mathematics and Statistics 4:1, pages 55-62.
Crossref
Esmaeil ROSTAMI & Reza NEKOOEI. (2016) On a question about almost prime ideals. TURKISH JOURNAL OF MATHEMATICS 40, pages 620-623.
Crossref
Ayman BADAWI, Ünsal TEKİR, Emel ASLANKARAYİĞİT UĞURLU, Gülşen ULUCAK & Ece YETKİN ÇELİKEL. (2016) Generalizations of 2-absorbing primaryideals of commutative rings. TURKISH JOURNAL OF MATHEMATICS 40, pages 703-717.
Crossref
Emel Aslankarayigit Ugurlu, Fethi Callialp & Unsal Tekir. (2016) Prime, weakly prime and almost prime elements in multiplication lattice modules. Open Mathematics 14:1, pages 673-680.
Crossref
Ayman Badawi, Unsal Tekir & Ece Yetkin. (2015) ON WEAKLY 2-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS. Journal of the Korean Mathematical Society 52:1, pages 97-111.
Crossref
C. S. Manjarekar & A. V. Bingi. (2014) -Prime and -Primary Elements in Multiplicative Lattices . Algebra 2014, pages 1-7.
Crossref
Farkhonde Farzalipour. (2014) On Almost Semiprime Submodules. Algebra 2014, pages 1-6.
Crossref
Ayman Badawi, Unsal Tekir & Ece Yetkin. (2014) ON 2-ABSORBING PRIMARY IDEALS IN COMMUTATIVE RINGS. Bulletin of the Korean Mathematical Society 51:4, pages 1163-1173.
Crossref
S. Moradi & A. Azizi. (2013) n-almost prime submodules. Indian Journal of Pure and Applied Mathematics 44:5, pages 605-619.
Crossref
Hani A. Khashan. (2012) On almost prime submodules. Acta Mathematica Scientia 32:2, pages 645-651.
Crossref
NASER ZAMANI. (2009) φ-PRIME SUBMODULES. Glasgow Mathematical Journal 52:2, pages 253-259.
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.