A zero divisor graph determined by equivalence classes of zero divisors

Conic divisor classes over a normal monoid algebra

Let R=K[M] be a normal affine monoid algbera over a field K.Up to isomorphism the conic ideals are exactly the direct summands ofthe extension R^{1/n} of R. We show that the classes of the conic divisorial ideals can be identified with the full-dimensional open cells in a decomposition of a torus naturally associated with M. Furthermore, they can be characterized by the relative compactness of a certain group associated with them. Baetica has given examples of Cohen-Macaulay divisorial ideals that are not conic. Wereview his construction and streamline the arguments somewhat. In the last part …

Zero-Divisor Graphs and Zero-Divisor Functors

Inspired by a very recent work of A. Ðurić, S. Jevđenić and N. Stopar, we introduce a new definition of zero-divisor graphs attached to rings, that includes all of the classical definitions already known in the literature. We provide an interpretation of such graphs as images of a functor, that we call zero-divisor functor and which is associated with a family of special equivalence relations fixed beforehand. We thus recover and generalize many known results for zero-divisor graphs and provide a framework which might be useful for further investigations on this topic.

Auslander class, $\g_C$ and $C$--projective modules modulo exact zero-divisors

For a semidualizing module $C$ over a ring $R$, we study the following classes modulo exact zero divisors: $\g_C$--projectives, $\mathcal G_C$; the Auslander class $\mathcal A_C$; the Bass class $\mathcal B_C$; $\mathcal{P}_C$--projective; $ {\mathcal F}_C$--projective; and ${\mathcal I}_C$--injective dimensions.

离散多面拟阵的除子类群

The divisor class group of a discrete polymatroid

本文研究离散多面拟阵的环面环，给出正规情形下除子类群与典范模类的计算方法，并对多类多面拟阵进行深入分析。

On reduced zero-divisor graphs of posets

In this paper we study some of the basic properties of a graph which is constructed from the equivalence classes of non-zero zero-divisors determined by annihilator ideals of a poset. In particular, we demonstrate how this graph helps in identifying the annihilator prime ideals of a poset that satisfies the ascending chain condition for its proper annihilator ideals.

Conditions for stable range of an elementary divisor rings

Using the concept of ring of Gelfand range 1 we proved that a commutative Bezout domain is an elementary divisor ring iff it is a ring of Gelfand range 1. Obtained results give a solution of problem of elementary divisor rings for different classes of commutative Bezout domains, in particular, $PM^{*}$, local Gelfand domains and so on.