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Article
Finitely generated projective modules over exchange rings
This paper studies finitely generated projective modules over exchange rings. We prove that cancellation holds inp(R), andK o (R) is completely determined by the continuous maps fr...
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Article
A New Graph Structure of Commutative Semigroups
In this paper, a new zero-divisor graph $\overline{\G}(S)$ is defined and studied for a commutative semigroup $S$ with zero element. The properties and the structure of the graph are studied; for any complete ...
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Article
The structure of a class of Z-local rings
A local ring R is called Z-local if J(R) = Z(R) and J(R)2 = 0. In this paper the structure of a class of Z-local rings is determined.
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Article
The structure of zero-divisor semigroups with graph K n ○K 2
This paper determines all commutative zero divisor semigroups whose zero divisor graph is a complete graph (finite or infinite), or a complete graph (finite or infinite) with one additional end vertex, and gi...
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Article
The Zero-divisor Graphs of Posets and an Application to Semigroups
In this paper, we introduce the notion of a compact graph. We show that a simple graph is a compact graph if and only if G is the zero-divisor graph of a poset, and give a new proof of the main result in Halaš an...
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Article
Classification of some τ-congruence-free completely regular semigroups
Let τ be an equivalence relation on a semigroup. We introduce τ-congruence-free semigroups, extending the notion of congruence-free semigroups, and classify all completely regular semigroups which are τ-congruenc...
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Article
Zero divisors and prime elements of bounded semirings
A semiring is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse. A bounded semiring is a semiring equipped with a compatible bounded partial ...
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Article
On Reduction Numbers of Products of Ideals
Let R be a standard graded algebra over an infinite field \(\mathbb {K}\) K and M a finitely generated \({\mathbb Z}\) Z -graded R-module. Let \(I_1,\ldots I_m\) I 1 , … I m be graded ideals of R