In 1999, Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty and vagueness, and many researchers have created some models to solve problems in decision making and medical diagnosis. In this paper, we introduce the concept of soft Lie subalgebras (resp. soft Lie ideals) and state some of their fundamental properties. We also introduce t...

In this paper, the concept of (∈γ ,∈γ ∨qδ)-fuzzy soft hinterior ideals over a hemiring is introduced and investigated. Some characterization theorems of h-semisimple hemirings are derived in terms of (∈γ ,∈γ ∨qδ)-fuzzy soft left (right) h-ideals and (∈γ ,∈γ ∨qδ)-fuzzy soft hinterior ideals. 2010 AMS Classification: 20M12, 08A72

We present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the integers. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals resp. over finite fields, and the idea of Shimoyama–Yokoyama resp. Eisenbud– Hunecke–Vasconcelos to extract primary ideals from pseudo–primary ideals. A parallelized version of the algor...

We extend to bimodules Schelter’s localization of a ring with respect to Gabriel filters of left and right ideals. Our two-sided localization of bimodules provides an endofunctor on a convenient bicategory of rings with filters of ideals. This is used to study the Picard group of a ring relative to a filter of ideals.

Denote by PSelf Ω (resp., Self Ω) the partial (resp., full) transformation monoid over a set Ω, and by SubV (resp., EndV ) the collection of all subspaces (resp., endomorphisms) of a vector space V . We prove various results that imply the following: (1) If cardΩ > 2, then Self Ω has a semigroup embedding into the dual of Self Γ iff card Γ > 2 . In particular, if Ω has at least two elements, th...

We study the state complexity of binary operations on regular languages over different alphabets. It is known that if L′m and Ln are languages of state complexities m and n, respectively, and restricted to the same alphabet, the state complexity of any binary boolean operation on L′m and Ln is mn, and that of product (concatenation) is m2 n − 2n−1. In contrast to this, we show that if L′m and L...

Let $R$ be a commutative ring with identity and $N(R)$ and
 $J\left(R\right)$ denote the nilradical Jacobson radical
 of $R$, respectively. A proper ideal $I$ is called an
 n-ideal if for every $a,b\in R$, whenever $ab\in I$\ $a\notin
 N(R)$, then $b\in I$. In this paper, we introduce study
 J-ideals as new generalization n-ideals in rings.
 $I$\ $R$\ J-ideal $ab\i...

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 th...

After the ring theoretic study of diierential operators in positive characteristic by S.U. Chase and S.P. Smith, B. Haastert started investigation of D-modules on smooth varieties in positive characteristic, and the work of R. BBgvad followed. The purpose of this paper is to complement some basics for further study. We x an algebraically closed eld k of positive characteristic p. All the variet...