Some Study of Semigroups of h-Bi-Ideals of Semirings

Mathematical Problems in Engineering

The main aim of this research is to introduce Left h − Clifford Semi-rings. Using some basic properties of h − regular semi-rings we shall investigate several properties of Left h − Clifford semi-rings and their characterizations. We will also establish that a semi-group Q will be a Left Clifford Semi-group iff the semi-group P (Q) of all subsets of Q is a Left h − Clifford Semiring. Also, this research will investigate the distributive congruences of regular semi-rings.

International Journal of Algebra, 2010

The concepts of h-prime ideals and h-semiprime ideals in semirings and Γ-semirings are introduced so that their properties are studied. In particular, the relationships between Γ-semirings and its related operator semirings are described in terms of the h-closure; the h-prime and h-semiprime ideals. These results will be used to obtain some other new results such as the inclusion preserving bijections between the h-prime (or h-semiprime) ideals of a Γ-semiring and its related operator semirings. Moreover, the h-regularity and the H-Noetherian Γ-semirings will be characterized. Some recent results given by T. K. Dutta and S. K. Sardar in semiprime ideals and irreducible ideals of a Γ-Semirings and extended and generlized.

Commentationes Mathematicae Universitatis Carolinae, 1984

Regular and orthodox ring-semigroups and semirings arT^EaracteriBed, as well as ring-semigroups with chain conditions on idempotents and principal ideals. Congruences on additively regular semirings are also considered.

Bi ideals are the generalization of quasi ideals which are themselves the generalization of the so called one-sided, right and left ideals. In this paper, we define the m-bi ideals as a generalization of the bi ideals. The important properties of the m-bi ideals from the pure algebraic point of view have been described. Moreover, we present the form of the m-bi ideals generated by subsets of the semiring. On the basis of these properties, further characterizations of the semiring will be helpful.

In this paper, we study the class of Right regular and Multiplicatively subidempotent semirings. Especially we have focused on the additive identity ‘e’ which is also multiplicative identity in both semirings.

We define semigroup semirings by analogy with group rings and semigroup rings. We develop arithmetic properties and determine sufficient conditions under which a semigroup semiring is atomic, has finite factorization, or has bounded factorization. We also present a semigroup semiring analog (though not a generalization) of Gauss' lemma on primitive polynomials.

In this paper, we have characterized a semigroup that is a semilattice of left (right) simple semigroups, a semigroup that is a semilattice of left (right) groups in terms of anti fuzzy left (right, two-sided) ideals, anti fuzzy (generalized) bi-ideals, anti fuzzy interior ideals and anti fuzzy quasi-ideals. Keywor

In this paper we have focused on the additive and multiplicative identity " e " and determine the additive and multiplicative semigroups. Here we established that, A semiring S in which (S, +) and (S, •) are left singular semigroups, then S is a left regular semiring. We have framed an example for this proposition by considering a two element set.

2015

In this work, we attempt to investigate the connection between various types of ideals (for examples (m;n)-ideal, bi-ideal, interior-ideal, quasi-ideal, prime-ideal and maximal-ideal) of an or- dered semigroup (S; � ; � ) and the corresponding, hyperideals of its EL-hyperstructure (S; � ) (if exists). Moreover, we construct the class of EL--semihypergroup, associated to a partially-ordered - semigroup.

Semigroup Forum, 1996