Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by Γ′(R), is a graph with vertices in W ∗(R), which is the set of all non-zero and non-unit elements of R, and two distinct vertices a and b in W ∗(R) are adjacent if and only if a / ∈ bR and b / ∈ aR. In this paper, we characterize all commutative rings whose cozero-divisor graphs are forest, star, doubl...

Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by , is a graph with vertices in   R     W R  , which is the set of all non-zero and non-unit elements of R, and two distinct vertices a and b in are adjacent if and only if and   W R  a bR  b aR  . In this paper, we investigate some combinatorial properties of the cozero-divisor graphs    ...

Let [Formula: see text] be a commutative ring with unity. The prime ideal sum graph of the is simple undirected whose vertex set nonzero proper ideals and two distinct vertices are adjacent if only text]. In this paper, we characterize all finite non-local rings genus

This talk will provide a snapshot of contemporary commutative algebra. In classical commutative algebra and algebraic number theory, the Dedekind domains are the most important class of rings. Modern commutative algebra studies numerous generalizations of the Dedekind domains in attempts to generalize results of algebraic number theory. This talk will introduce a few important generalizations o...