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Communications in Algebra Volume 28, 2000 - Issue 2
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Original Articles

On ideals consisting entirely of zero divisors

F. Azarpanah Department of Mathematics, Chamran University, Ahvaz, Iran
,
O.A.S. Karamzadeh Department of Mathematics, Chamran University, Ahvaz, Iran
&
Rezai A. Aliabad Institute for Studies in Theoretical Physics and Mathematics, Tehran
Pages 1061-1073 | Received 01 Oct 1998, Published online: 27 Jun 2007

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Z. Arjmandnezhad, F. Azarpanah, A.A. Hesari & A.R. Salehi. (2022) Characterizations of maximal z°-ideals of C(X) and real maximal ideals of q(X). Quaestiones Mathematicae 45:10, pages 1575-1587.
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F. Azarpanah, R. Mohamadian & P. Monjezi. (2022) On z-ideals of C(X). Quaestiones Mathematicae 45:6, pages 859-873.
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Sudip Kumar Acharyya, Rakesh Bharati & A. Deb Ray. (2021) Rings and subrings of continuous functions with countable range. Quaestiones Mathematicae 44:6, pages 829-848.
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Sudip Kumar Acharyya, Sagarmoy Bag, Goutam Bhunia & Pritam Rooj. (2019) Some new results on functions in C(X) having their support on ideals of closed sets. Quaestiones Mathematicae 42:8, pages 1079-1090.
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E. Hashemi, M. Abdi & A. Alhevaz. (2017) On the diameter of the compressed zero-divisor graph. Communications in Algebra 45:11, pages 4855-4864.
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Ebrahim Ghashghaei & Warren Wm. McGovern. (2017) Fusible rings. Communications in Algebra 45:3, pages 1151-1165.
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A.R. Aliabad & R. Mohamadian. (2011) On SZ°-Ideals in Polynomial Rings. Communications in Algebra 39:2, pages 701-717.
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Themba Dube & Mack Matlabyane. (2009) Notes Concerning Characterizations of Quasi-F Frames. Quaestiones Mathematicae 32:4, pages 551-567.
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M. Ghirati & O. A. S. Karamzadeh. (2008) On Strongly Essential Submodules. Communications in Algebra 36:2, pages 564-580.
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Articles from other publishers (32)

M. Abdi & Y. Talebi. (2023) On the diameter of the zero-divisor graph over skew PBW extensions. Journal of Algebra and Its Applications 23:05.
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Khaled Alhazmy, Fuad Ali Ahmed Almahdi, El Mehdi Bouba & Mohammed Tamekkante. (2023) On 2 r -ideals in commutative rings with zero-divisors . Open Mathematics 21:1.
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R. Mohamadian. (2023) Countable Strongly Annihilated Ideals in Commutative Rings. Bulletin of the Iranian Mathematical Society 49:3.
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R. K. Sharma & Amit B. Singh. (2022) On rings with weak property (A) and their extensions. Journal of Algebra and Its Applications 22:05.
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Faranak Farshadifar. (2023) Strong -Submodules of a Module . Journal of Mathematics 2023, pages 1-5.
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Khaled Alhazmy, Fuad AlmahdiAliAli, El BoubaMehdiMehdi & Mohammed Tamekkante. (2023) On strongly r-ideals on commutative rings and some related graphs. Filomat 37:15, pages 5027-5038.
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Sudip Kumar Acharyya, Atasi Deb Ray & Pratip Nandi. (2021) Ordered Field Valued Continuous Functions with Countable Range. Bulletin of the Iranian Mathematical Society 48:2, pages 1-14.
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E. Ghashghaei. (2020) Variations of essentiality of ideals in commutative rings. Journal of Algebra and Its Applications 21:03.
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Mehdi Badie. (2020) On $$\mathcal {H}_Y$$-Ideals. Bulletin of the Iranian Mathematical Society 47:4, pages 1081-1095.
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Themba Dube & Mehdi Parsinia. (2020) On the Sum of $$z^\circ $$-Ideals in Two Classes of Subrings of C(X). Bulletin of the Iranian Mathematical Society 47:4, pages 1069-1080.
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Abdelhaq El Khalfi, Najib Mahdou & Aziza Rahmouni Hassani. (2020) Bi-amalgamation of rings defined by certain annihilator conditions. Rocky Mountain Journal of Mathematics 50:3.
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Mostafa Abedi. (2019) Some Notes on z-Ideal and d-Ideal in $$\mathcal {R}L$$. Bulletin of the Iranian Mathematical Society 46:3, pages 593-611.
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F. Azarpanah, A.A. Hesari & A.R. Salehi. (2020) Computation of depth in C(X). Journal of Algebra 550, pages 54-68.
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Ali Rezaei ALİABAD, Mehdi BADİE & Sajad NAZARİ. (2020) An extension of $z$-ideals and $z^\circ$-ideals. Hacettepe Journal of Mathematics and Statistics 49:1, pages 254-272.
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Sudip Kumar Acharyya, Sagarmoy Bag & Joshua Sack. (2019) Ideals in rings and intermediate rings of measurable functions. Journal of Algebra and Its Applications 19:02, pages 2050038.
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Themba Dube & Lindiwe Sithole. (2019) On the sublocale of an algebraic frame induced by the d-nucleus. Topology and its Applications 263, pages 90-106.
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Ebrahim Hashemi, Mona Abdi & Abdollah Alhevaz. (2019) On diameter of the zero-divisor and the compressed zero-divisor graphs of skew Laurent polynomial rings. Journal of Algebra and Its Applications 18:07, pages 1950126.
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Esmaeil Rostami, Masoumeh Hedayati & Nosratollah Shajareh Poursalavati. (2019) The flat topology on the minimal and maximal prime spectrum of a commutative ring. Journal of Algebra and Its Applications 18:06, pages 1950110.
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F. Azarpanah, D. Esmaeilvandi & A.R. Salehi. (2019) Depth of ideals of C(X). Journal of Algebra 528, pages 474-496.
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Sagarmoy Bag, Sudip Kumar Acharyya & Dhananjoy Mandal. (2019) A class of ideals in intermediate rings of continuous functions. Applied General Topology 20:1, pages 109.
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E. Hashemi, A. As. Estaji & A. Alhevaz. (2016) On Ore extension and skew power series rings with some restrictions on zero-divisors. Journal of Algebra and Its Applications 16:09, pages 1750164.
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E. Hashemi, A. AS. Estaji & M. Ziembowski. (2017) Answers to Some Questions Concerning Rings with Property ( A ) . Proceedings of the Edinburgh Mathematical Society 60:3, pages 651-664.
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F. Azarpanah & A.R. Salehi. (2016) Ideal structure of the classical ring of quotients of C(X). Topology and its Applications 209, pages 170-180.
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Rasul Mohammadi, Ahmad Moussavi & Masoome Zahiri. (2016) ON ANNIHILATIONS OF IDEALS IN SKEW MONOID RINGS. Journal of the Korean Mathematical Society 53:2, pages 381-401.
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Themba Dube & Jissy Nsonde Nsayi. (2015) When certain prime ideals in rings of continuous functions are minimal or maximal. Topology and its Applications 192, pages 98-112.
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Najib Mahdou & Aziza Rahmouni Hassani. (2010) On Strong (A)-Rings. Mediterranean Journal of Mathematics 9:2, pages 393-402.
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Chan Yong Hong, Nam Kyun Kim, Yang Lee & Pace P. Nielsen. (2009) The minimal prime spectrum of rings with annihilator conditions. Journal of Pure and Applied Algebra 213:7, pages 1478-1488.
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Chan Yong Hong, Nam Kyun Kim, Yang Lee & Sung Ju Ryu. (2007) Rings with Property (A) and their extensions. Journal of Algebra 315:2, pages 612-628.
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Karim Samei. (2007) The zero-divisor graph of a reduced ring. Journal of Pure and Applied Algebra 209:3, pages 813-821.
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F. Azarpanah & R. Mohamadian. (2006) $$ {\sqrt z } $$ –Ideals and $$ {\sqrt {z^{ \circ } } } $$ –Ideals in C(X). Acta Mathematica Sinica, English Series 23:6, pages 989-996.
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Ali Rezaei Aliabad. (2006) Pasting topological spaces at one point. Czechoslovak Mathematical Journal 56:4, pages 1193-1206.
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F. Azarpanah & M. Karavan. (2005) On nonregular ideals and z°-ideals in C(X). Czechoslovak Mathematical Journal 55:2, pages 397-407.
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