Semirings have been studied by various researchers either in an attempt to broaden the
techniques coming from semigroup theory or generalization of group theory and ring theory …

From an algebraic point of view, semirings provide the most natural generalization of group
theory and ring theory. In the absence of additive inverses, one has to impose some weaker …

In [3, p. 270], R. Gilmer addresses the problem of determining when a commutative
semigroup ring R [S] is a principal ideal ring. In [6], a characterization was deduced for zero …

Pime ideals play very important role in semigroups and are rooted from prime numbers of
the integers. Especially, it is cornerstone on commutative rings and topological semigroups …

D-semisimple, then R is D-semisimple, too. The aim of this paper is to obtain an analogous
result for rings graded by inverse semigroups. A semigroup S is said to be inerse if for every …

When is the Semigroup Ring Perfect? Page 1 PROCEEDINGS OF THE AMERICAN
MATHEMATICAL SOCIETY Volume 89, Number 1, September 1983 WHEN IS THE SEMIGROUP …

Throughout this paper the ring R and the semigroup S are commutative with identity;
moreover, it is assumed that S is cancellative, ie, that S can be embedded in a group. The …

The theory of primary ideals played an important role in commutative ring theory and later it
was extended to commutative semigroups. In this paper we develop the theory of primary …

We use the term semigroup to mean a commutative multiplicative semigroup with 0 and I. An
ideal I in a semigroup S is a nonempty subset I~ S with SI~ I (and hence SI= I since i ES) …

Let S be a semilsttice o_~ f semigroups S (~ Y), an d let. R be a ring. How to characterize
some ring properties of s semigroup~ R (S) in terms of rings R ($~)? In the present paper this …