Very strong multiplication ideals and the ideal θ(I) over a commutative semirings

Let R a commutative semiring with identity. An ideal I is called a multiplication ideal if every ideal contained in I is a multiple of I. We consider the associated ideal θ(I). It is proved that the strong ideal θ(I) is important in the study of multiplication ideals. Among various applications given, the following results are proved: if I is a faithful very strong multiplication ideal, then the strong ideal θ(I) is an idempotent ideal of R such that θ(θ(I)) = θ(I), and every secondary representable ideal of R which is also a very strong multiplication ideal is finitely generated

An ideal based zero-divisor graph of a commutative semiring

There is a natural graph associated to the zero-divisors of a commutative semiring with non-zero identity. In this article we essentially study zero-divisor graphs with respect to primal and non-primal ideals of a commutative semiring R and investigate the interplay between the semiring-theoretic properties of R and the graph-theoretic properties of ΓI(R) for some ideal I of R. We also show that the zero-divisor graph with respect to primal ideals commutes by the semiring of fractions of R

GG-supplemented property in the lattices

summary:Let $L$ be a lattice with the greatest element $1$. Following the concept of generalized small subfilter, we define $g$-supplemented filters and investigate the basic properties and possible structures of these filters

On primarily multiplication modules over pullback rings

The purpose of this paper is to present a new approach to the classification of indecomposable primarily multi-plication modules with finite-dimensional top over pullback of two Dedekind domains. We extend the definition and results given in [10] to a more general primarily multiplication modules case

Weak comultiplication modules over a pullback of commutative local Dedekind domains

The goal point of recent attempts to classify indecomposable modules over non-artinian rings has been pullback rings. The purpose of this paper is to outline a new approach to the classification of indecomposable weak comultiplication modules with finite-dimensional top over certain kinds of pullback rings

The ideal theory in the quotients of semirings

Since the theory of ideals plays an important role in the theory of quotient semirings, in this paper, we will make an intensive study of the notions of Noetherian, Artinian, prime, primary, weakly primary and k-maximal ideals in commutative quotient semirings. The bulk of this paper is devoted to stating and proving analogues to several well-known theorems in the theory of the residue class rings

On DPA-Resistive Implementation of FSR-based Stream Ciphers using SABL Logic Styles

The threat of DPA attacks is of crucial importance when designing cryptographic hardware. This contribution discusses the DPA-resistant implementation of two eSTREAM finalists using SABL logic styles. Particularly, two Feedback Shift Register (FSR) based stream ciphers, Grain v.1 and Trivium are designed in both BSim3 130nm and typical 350nm technologies and simulated by HSpice software. Circuit simulations and statistical power analysis show that DPA resistivity of SABL implementation of both stream ciphers has a major improvement. The paper presents the tradeoffs involved in the circuit design and the design for performance issues

On primal and weakly primal ideals over commutative semirings

Since the theory of ideals plays an important role in the theory of semirings, in this paper we will make an intensive study of the notions of primal and weakly primal ideals in commutative semirings with an identity 1. It is shown that these notions inherit most of the essential properties of the primal and weakly primal ideals of a commutative ring with non-zero identity. Also, the relationship among the families of weakly prime ideals, primal ideals and weakly primal ideals of a semiring R is considered

Corrigendum to "The ideal theory in quotients of commutative semirings"

This corrigendum is written to correct an error in the proof of the Theorem 2.16 of S. E. Atani [1]