Ideals in Ordered Γ-Semirings
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2018, Vol 38, Issue 1
Abstract
In this paper, we introduce the notion of k-ideal, m−k ideal, prime ideal, maximal ideal, filter, irreducible ideal, strongly irreducible ideal in ordered Γ-semirings, study the properties of ideals in ordered Γ-semirings and the relations between them. We characterize m − k ideals using derivation of ordered Γ-semirings and prove that every ideal in a mono regular ordered Γ-semiring is a prime ideal and field ordered Γ-semiring is simple.
Authors and Affiliations
Marapureddy Murali Krishna Rao
Keywords
Related Articles
- EP ID EP394542
- DOI 10.7151/dmgaa.1284
- Views 37
- Downloads 0
ON L-FUZZY MULTIPLICATION MODULES
Let L be a complete lattice. In a manner analogous to a commutative ring, we introduce and investigate the L-fuzzy multiplication modules over a commutative ring with non-zero identity. The basic properties of the prime...
Weak-hyperlattices derived from fuzzy congruences
In this paper we explore the connections between fuzzy congruence relations, fuzzy ideals and homomorphisms of hyperlattices. Indeed, we introduce the concept of fuzzy quotient set of hyperlattices as it was done in the...
ON THE GENUS OF THE CAYLEY GRAPH OF A COMMUTATIVE RING
Let R be a commutative ring with non-zero identity and let Z(R) be the set of all zero-divisors. The Cayley graph CAY(R) of R is the simple undirected graph whose vertices are elements of R and two distinct vertices x an...
ON A PERIODIC PART OF PSEUDO-BCI-ALGEBRAS
In the paper the connections between the set of some maximal elements of a pseudo-BCI-algebra and deductive systems are established. Using these facts, a periodic part of a pseudo-BCI-algebra is studied.
Completely Archimedean Semirings
In this paper we give a structural description of completely Archimedean semirings which is an extension of the structure theorem of completely Archimedean semigroups.