Commutative rings
Uniformly 2-absorbing primary ideals of commutative rings
... of commutative rings, which imposes a certain boundedness condition on the usual notion of 2-absorbing primary ideals of commutative ...of commutative rings with ...
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Noncommutative (Crepant) Desingularizations and the Global Spectrum of Commutative Rings
... for commutative rings and rational singularities ...graded rings, we derive a criterion which tells whether their normalizations have rational singularities, using the ...
32
Associated Graphs of Modules Over Commutative Rings
... Abstract. Let R be a commutative ring with identity and let M be an R-module. In this paper we introduce a new graph associated to modules over commutative rings. We study the relationship between ...
14
Exact annihilating-ideal graph of commutative rings
... of commutative rings studied in [5] and [6], we define exact annihilating-ideal graph EAG(R) of a commutative ring R to be an undirected graph whose vertex set is the set of nonzero exact ...
7
On the Structure of Commutative Rings with ${\bf {p_1}^{k_1}\cdots {p_n}^{k_n} Zero-Divisors
... on rings R with |Z(R)| = p k where p is a prime number and k ≥ ...finite commutative ring R is local if and only if |Z(R)| = p k and |R| = p n for some prime number p and n > k ≥ 0 (Theorem ...
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General Parametrization of Stabilizing Controllers with Doubly Coprime Factorizations over Commutative Rings
... a) Commutative Rings: We will consider that the set of all stable causal transfer functions is a commutative ring, denoted by A ...the commutative ring A is an integral domain, F becomes a ...
6
On Weakly 2-Absorbing Semi-Primary Submodules of Modules over Commutative Rings
... The concept of weakly prime submodule was introduced and studied by Behboodi and Koohi [5]. We recall that a proper submodule N of M is called a weakly prime submodule, if 0 6= rm ∈ N , where r ∈ R, m ∈ M , then m ∈ N or ...
14
On the Cozero Divisor Graphs of Commutative Rings
... and R were studied in [6]. In this paper, we study the cozero-divisor graphs of the rings of polynomials, power series and the direct product of two arbitrary commutative rings. Also, we ...
7
Operads and Γ homology of commutative rings
... Proof. Again we give the details for homology. If B is flat over A and contains a field of characteristic zero then Harrison homology coincides with Andr´e–Quillen homology [3] so the result is given by Theorem 6·4. If B ...
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INTUITIONISTIC FUZZY 2-ABSORBING IDEALS OF COMMUTATIVE RINGS
... Abstract. The aim of this paper is to give a definition of an intu- itionistic fuzzy 2- absorbing ideal and an intuitionistic fuzzy weakly completely 2- absorbing ideal of commutative rings and to give ...
16
Quo Vadis Quaternion? Cryptanalysis of Rainbow over Non-Commutative Rings
... non-commutative ring and thus NC-Rainbow is not equally secure to Rainbow for every non-commutative ring (cf. lemma 2). But there might be smarter en- codings than Quaternions, which speed up known attacks ...
15
Finitely Generated Annihilating-Ideal Graph of Commutative Rings
... Throughout this paper, all rings are commuta- tive with identity and all modules are unital. For a ring R we denote by (R), (R), Z (R), I(R) and F (R) the set of all prime ideals, the set of all min- imal prime ...
9
Classical 2-absorbing Submodules of Modules Over Commutative Rings
... a commutative ring R is a u-ring provided R has the property that an ideal contained in a finite union of ideals must be contained in one of those ideals; and a um-ring is a ring R with the property that an ...
14
On the genus of the k annihilating ideal hypergraph of commutative rings
... linking commutative ring theory with graph theory has been started with the concept of the zero-divisor graph of a commutative ...a commutative ring and Z(R) ∗ be the set of all nonzero zero-divisors ...
15
On hereditary reducibility of 2-monomial matrices over commutative rings
... This paper is devoted to one class of monomial matrices over commu- tative rings which first arose in studying indecomposable representations of finite p-groups over local rings ([1]).. [r] ...
11
Indecomposable and irreducible \(t\)-monomial matrices over commutative rings
... [4] P. M. Gudivok, I. B. Chukhraj, On the number of indecomposable matrix rep- resentations of given degree of a finite p-group over commutative local rings of characteristic p s , Nauk. Visn. Uzhgorod ...
10
On the Structure of Commutative Rings with ${\bf {p_1}^{k_1}\cdots {p_n}^{k_n} Zero Divisors II
... divisors, where s is a positive integer, p i , s are distinct prime number and 1 ≤ k i ≤ 3 were determined. Also we determined the structure of nonlocal rings with p k zero-divisors where k = 4 or 5. In the paper ...
9
Commutative rings with homomorphic power functions
... Third, in the absence of commutativity, conditions i and ii in Theorem 4.5 do not imply m-linearity: consider the ring of upper triangular 2 x 2 matrices over a reduced m-linear ring in [r] ...
12
A note on the extended total graph of commutative rings
... Throughout this paper R is a commutative ring with nonzero iden- tity. Recently, there has been considerable attention in the work to associating graphs with algebraic structures (see [4],[5],[6], [8], [9] and ...
9
Decomposition of Automorphisms of Certain Solvable Subalgebra of Symplectic Lie Algebra over Commutative Rings
... 2 K. I. Beidar, M. Breˇsar, and M. A. Chebotar, “Jordan isomorphisms of triangular matrix algebras over a connected commutative ring,” Linear Algebra and Its Applications, vol. 312, no. 1–3, pp. 197–201, 2000. 3 ...
13