Results 101 to 110 of about 59,280 (204)
Filomat, 2017 In this paper, we present a new classes of ideals: called n-ideal. Let R be a commutative ring with nonzero identity. We define a proper ideal I of R as an n-ideal if whenever ab ? I with a ? ?0, then b ? I for every a,b ? R. We investigate some properties of n-ideals analogous with prime ideals. Also, we give many examples with regard to n-
Tekir, Unsal +2 more
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COMMUTATIVE WEAKLY INVO–CLEAN GROUP RINGS
Ural Mathematical Journal, 2019 A ring \(R\) is called weakly invo-clean if any its element is the sum or the difference of an involution and an idempotent. For each commutative unital ring \(R\) and each abelian group \(G\), we find only in terms of \(R\), \(G\) and their sections a ...
Peter V. Danchev
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Commutative Rings whose Matrix Rings are Baer Rings [PDF]
Proceedings of the American Mathematical Society, 1969 A ring R with unit element is a Baer ring if every left annihilator in R has the form Re, where e is an idempotent element. K. G. Wolfson has proven [3, Corollary 15], that if R is a Priifer ring (a commutative integral domain in which every finitely generated ideal is invertible) then the ring of endomorphisms of a finitely generated free module over ...
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A signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial rings
Open Mathematics, 2015 Signature-based algorithms are efficient algorithms for computing Gröbner-Shirshov bases in commutative polynomial rings, and some noncommutative rings. In this paper, we first define skew solvable polynomial rings, which are generalizations of solvable ...
Zhao Xiangui, Zhang Yang
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Non-commutative Henselian rings
Journal of Algebra, 2009 7 pages; Added references, email and postal ...
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Commutative Rings Behind Divisible Residuated Lattices
MathematicsDivisible residuated lattices are algebraic structures corresponding to a more comprehensive logic than Hajek’s basic logic with an important significance in the study of fuzzy logic.
Cristina Flaut, Dana Piciu
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On S-2-Prime Ideals of Commutative Rings
MathematicsPrime ideals and their generalizations are crucial in numerous research areas, particularly in commutative algebra. The concept of generalization of prime ideals begins with the study of weakly prime ideals.
Sanem Yavuz +3 more
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Finite Commutative Chain Rings
Finite Fields and Their Applications, 2001 A commutative ring with unit is called a chain ring if all its ideals form a chain under inclusion. All finite chain rings can be obtained in the following way: Let \(p\) be a prime, \(n,r>0\), \(f\in \mathbb{Z}_{p^n}[X]\) a monic polynomial, \(\deg(f)=r\) whose image in \(\mathbb{Z}_p[X]\) is irreducible and let \(\text{GR} (p^n,r): =\mathbb{Z}_{p^n ...
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On sM-Prime Ideals in Commutative Rings
AxiomsAll rings considered are commutative with identity, and all modules are assumed to be unital. In this paper, we study R-modules in which every quasi-primary submodule is also primary; we refer to such modules as satisfying condition (*).
Gülşen Ulucak +3 more
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