In this paper we investigate the parallelization of two modular algorithms. In fact, we consider the modular computation of Gröbner bases (resp. standard bases) and the modular computation of the associated primes of a zero–dimensional ideal and describe their parallel implementation in Singular. Our modular algorithms to solve problems over Q mainly consist of three parts, solving the problem ...

The notion of a BE-semigroup is introduced, and related properties are investigated. The concept of left resp., right deductive systems of a BE-semigroup is also introduced.

Good and Hughes [9] introduced the notion of bi-ideal and Steinfeld [11, 12] introduced the notion of quasi-ideal. Sioson [10] studied some properties of quasi-ideals of ternary semigroups. In [1], Dixit and Dewan studied about the quasi-ideals and bi-ideals of ternary semigroups. Quasi-ideals are generalization of right ideals, lateral ideals, and left ideals whereas bi-ideals are generalizati...

In this paper, we focus on the duo ring property via quasinilpotent elements, which gives a new kind of generalizations commutativity. We call rings qnil-duo. Firstly, some properties quasinilpotents in are provided. Then set is applied to rings, perspective, introduce and study right (resp., left) qnil-duo rings. show that concept not left-right symmetric. Among others, it proved if Hurwitz se...

A factor u of a word w is called right special if there exist two distinct letters a and b such that both ua and ub are factors of w. Left special factors are de)ned symmetrically. By Rw (resp. Lw) we denote the minimal natural number such that there is no right (resp. left) special factor of w of length Rw (resp. Lw). Moreover, Hw (resp. Kw) denotes the length of the shortest pre)x (resp. su,x...

The object of this paper is to prove that the standard categories in which homotopy theory is done, such as topological spaces, simplicial sets, chain complexes of abelian groups, and any of the various good models for spectra, are all homotopically self-contained. The left half of this statement essentially means that any functor that looks like it could be a tensor product (or product, or sma...

In this paper S will denote an AG-groupoid. A two-sided ideal I of S is called a right (left) pure ideal of S , if for each x in I , there is an element y in I such that ) = ( = x yx x xy . A left (right) pure ideal I is called purely prime if it is proper and if for any pure ideals 1 I and 2 I : I I I 2 1 implies I I1 or I I2 . Analogous to the construction of the pure spectrum of a semigroup ...

In this paper, the concept of (∈,∈ ∨ qk)-fuzzy quasi-ideals of an ordered semigroup S is introduced by the ordered fuzzy points of S, which is a generalization of fuzzy quasi-ideal of S, and related properties are investigated. Furthermore, we introduce the concepts of prime and completely semiprime (∈,∈ ∨ qk)-fuzzy quasi-ideals of ordered semigroups, and characterize bi-regular ordered semigro...

let $s$ be an ordered semigroup. a fuzzy subset of $s$ is anarbitrary mapping   from $s$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. in this paper,  the concept of fuzzygeneralized bi-ideals of an ordered semigroup $s$ is introduced.regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.finally, two m...

In this paper, we establish some equivalent conditions for a semigroup to be regular and intra-regular, in terms of hybrid ideals bi-ideals. We also characterize the left right simple completely semigroups utilizing show that S is if only it simple. prove then each ideal ˜jµ S, have ˜jµ(r1r2) = ˜jµ(r2r1) all r1, r2 ∈ S.