RINGS IN WHICH EVERY NONZERO S-WEAKLY PRIME IDEAL IS S-PRIME
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In this paper, we introduce and study a new class of rings with multiplicative subset S which we’ll call S-WP-rings. A ring R with a multiplicative subset S is said to be S-WPring if every nonzero S-weakly prime ideal is S-prime. We next study the possible transfer of the properties of being S-WP-ring in the homomorphic image, in the localization, in the trivial ring extensions and the amalgamated algebra along an ideal introduced and studied by the authors of [5, 6, 7, 8]. Our results allow us to construct new original class of S-WP-rings subject to various ring theoretical properties.
Abstract
In this paper, we introduce and study a new class of rings with multiplicative subset S which we’ll call S-WP-rings. A ring R with a multiplicative subset S is said to be S-WPring if every nonzero S-weakly prime ideal is S-prime. We next study the possible transfer of the properties of being S-WP-ring in the homomorphic image, in the localization, in the trivial ring extensions and the amalgamated algebra along an ideal introduced and studied by the authors of [5, 6, 7, 8]. Our results allow us to construct new original class of S-WP-rings subject to various ring theoretical properties.
참고문헌 (19)
- F. A. Almahdi, "On weakly S-prime ideals of commutative rings", Analele Stiint. ale Univ. Ovidius Constanta Ser. Mat, 29(2), pp.173~186 (2021)
- D. D. Anderson, "Weakly prime ideals", Houston J. Math, 29(4), pp.831~840 (2003)
- D. D. Anderson, "Idealization of a module", J. Commut. Algebra, 1(1), pp.3~56 (2009)
- C. Bakkari, "Trivial extension definided by Pr¨ufer conditions", J. Pure App. Algebra, 214(1), pp.53~60 (2010)
- M. D’Anna, "Construction of Gorenstein rings", J. Algebra, 306(2), pp.507~519 (2006)
- M. D’Anna, "Comm. Algebra and Applications", pp.241~252 (2009), Walter De Gruyter
- M. D’Anna, "An amalgamated duplication of a ring along an ideal: the basic properties", J. Algebra Appl., 6(3), pp.443~459 (2007)
- M. D’Anna, "Properties of chains of prime ideals in amalgamated algebras along an ideal", J. Pure Appl. Algebra, 214, pp.1633~1641 (2010)
- A. El Khalfi, "Amalgamation extension in commutative ring theory : a survey", Moroccan Journal of Algebra and Geometry with Applications, 1(1), pp.139~182 (2022)
- A. El Khalfi, "Rings in which every nonzero weakly prime ideal is prime", Sao Paulo J. Math. Sci, 14(2), pp.689~697 (2020)
- S. Glaz, "Commutative Coherent Rings" (1989), Springer-Verlag
- A. Hamed, "S-prime ideals of a commutative ring Beitr", Algebra Geom, 61(3), pp.533~542 (2020)
- "Moroccan Journal of Algebra and Geometry with Applications", 2022, 183~188
- J. A. Huckaba, "Commutative Coherent Rings with Zero Divisors" (1988), Marcel Dekker
- S. Kabbaj, "Trivial Extensions Defined by Coherent-like Conditions", Comm. Algebra, 32(10), pp.3937~3953 (2004)
- S. Kabbaj, "Matlis’ semi-regularity and semi-coherence in trivial ring extensions:a survey", Moroccan Journal of Algebra and Geometry with Applications, 1(1), pp.1~17 (2022)
- H. Kim, "Foundations of Commutative rings and their Modules" (2016), Springer
- N. Mahdou, "On S-weakly prime ideals of commutative rings", Georgian Mathematical Journal (2022)
- M. Nagata, "Local rings", Interscience Tracts in Pure and Appl. Math. (1962)