Integration in semirings

2015

access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Motivated by some works on derivations on rings, Chandramouless-waran and Thiruveni discussed the notion of derivations on semirings. In this paper, we discuss the notion of right derivations on semirings and prove some simple properties. Mathematics Subject Classification: 16Y60

Motivated by some works on derivations on rings, Chandramoulesswaran and Thiruveni discussed the notion of derivations on semirings. In this paper, we discuss the notion of right derivations on semirings and prove some simple properties.

2015

Abstract: Motivated by some works on derivations on rings, Chandramouleeswaran and Thiruveni discussed the notion of derivations on semirings. In this paper, we introduce the notion of reverse derivations on semirings and prove some simple properties.

International Journal of Pure and Apllied Mathematics, 2015

Motivated by some works on derivations on rings, Chandramouleeswaran and Thiruveni discussed the notion of derivations on semirings. In this paper, we introduce the notion of reverse derivations on semirings and prove some simple properties.

Mathematica Slovaca, 2019

Basic algebras were introduced by Chajda, Halaš and Kühr as a common generalization of MV-algebras and orthomodular lattices, i.e. algebras used for formalization of non-classical logics, in particular the logic of quantum mechanics. These algebras were represented by means of lattices with section involutions. On the other hand, classical logic was formalized by means of Boolean algebras which can be converted into Boolean rings. A natural question arises if a similar representation exists also for basic algebras. Several attempts were already realized by the authors, see the references. Now we show that if a basic algebra is commutative then there exists a representation via certain semirings with involution similarly as it was done for MV-algebras by Belluce, Di Nola and Ferraioli. These so-called basic semirings, their ideals and congruences are studied in the paper.

International Journal of Mathematics Trends and Technology, 2017

This paper contains some results on connected semirings and b-lattice semirings. We consider a connected semiring (s,+,.,0) satisfying the identity 1+y=y+1 =1 for all y in s in which s is a variant of semi group (or) a-connected semigroup then it is proved that (s,a) is I-Medial, I-Semi Medial, Quasive separative.weakly separative. (S,.) is singular if (S,.) is rectangular band.Again we consider the same identity with (S,.

arXiv: Rings and Algebras, 2011

In this paper, among other results, there are described (complete) simple-simultaneously ideal-and congruence-simple-endomorphism semirings of (complete) idempotent commutative monoids; it is shown that the concepts of simpleness, congruence-simpleness and ideal-simpleness for (complete) endomorphism semirings of projective semilattices (projective complete lattices) in the category of semilattices coincide iff those semilattices are finite distributive lattices; there are described congruence-simple complete hemirings and left artinian congruence-simple complete hemirings. Considering the relationship between the concepts of 'Morita equivalence' and 'simpleness' in the semiring setting, we have obtained the following results: The ideal-simpleness, congruencesimpleness and simpleness of semirings are Morita invariant properties; A complete description of simple semirings containing the infinite element; The representation theorem-"Double Centralizer Property"-for simple semirings; A complete description of simple semirings containing a projective minimal onesided ideal; A characterization of ideal-simple semirings having either infinite elements or a projective minimal one-sided ideal; A confirmation of Conjecture of [18] and solving Problem 3.9 of [17] in the classes of simple semirings containing either infinite elements or projective minimal left (right) ideals, showing, respectively, that semirings of those classes are not perfect and the concepts of 'mono-flatness' and 'flatness' for semimodules over semirings of those classes are the same. Finally, we give a complete description of ideal-simple, artinian additively idempotent chain semirings, as well as of congruence-simple, latticeordered 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.

An. St. Univ. Ovidius Constanta, 2010

In this paper, we give semiring version of some classical results in commutative algebra related to Euclidean rings, PIDs, UFDs, G-domains, and GCD and integrally closed domains.

Journal of Advances in Mathematics, 2011

In this paper mainly we have obtained equivalent conditions on semirings, regular semirings and Idempotent semirings.

2004

Semirings are algebraic structures with two associative binary operations, where one distributes over the other, introduced by Vandiver [10] in 1934. In more recent times semirings have been deeply studied, especially in relation with applications ([5]). For example semirings have been used to model formal languages and automata theory (see [4]), to deal with scheduling problems ([3]) and semirings over real numbers ((max,+)-semirings) are the basis for the idempotent analysis [7].

Proceedings of the American Mathematical Society, 1964

By a topological semiring we mean a Hausdorff space S together with two continuous associative operations on S such that one (called multiplication) distributes across the other (called addition). That is, we insist that x(y+z)=xy+xz and (x+y)z = xz+yz for all x, y, and z in S. Note that, in contrast to the purely algebraic situation, we do not postulate the existence of an additive identity which is a multiplicative zero. In this note we point out a rather weak multiplicative condition under which each additive subgroup of a compact semiring is totally disconnected. We also give several corollaries and examples.

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.

Log. J. IGPL, 2018

In a previous article by two of the present authors and S. Bonzio, \L ukasiewicz near semirings were introduced and it was proven that basic algebras can be represented (precisely, are term equivalent to) as near semirings. In the same work it has been shown that the variety of \L ukasiewicz near semirings is congruence regular. In other words, every congruence is uniquely determined by its $0$-coset. Thus, it seems natural to wonder wether it could be possible to provide a set-theoretical characterization of these cosets. This article addresses this question and shows that kernels can be neatly described in terms of two simple conditions. As an application, we obtain a concise characterization of ideals in \L ukasiewicz semirings. Finally, we close this article with a rather general Cantor-Bernstein type theorem for the variety of involutive idempotent integral near semirings.