If one of the axioms in ring, namely inverse axiom addition operation, is omitted, it will produce another algebraic structure, a semiring. Analogous to there are zero elements, ideal (left/right) semiring, and cross product semiring ideal. The analog fuzzy has (left/right), associated with membership value. This paper discuss cross-product two (more) ideals from Furthermore, always be But conv...

The concept of soft translations of soft subalgebras and soft ideals over BCI/BCK-algebras is introduced and some related properties are studied. Notions of Soft extensions of soft subalgebras and soft ideals over BCI/BCK-algebras are also initiated. Relationships between soft translations and soft extensions are explored.

In this paper, we first introduce the new concept of completely semiprime fuzzy ideals of an ordered semigroup S, which is an extension of completely semiprime ideals of ordered semigroup S, and investigate some its related properties. Especially, we characterize an ordered semigroup that is a semilattice of simple ordered semigroups in terms of completely semiprime fuzzy ideals of ordered semi...

In this note, we show in the line of [3] that an ordered Γ-semigroup is left and right simple if and only if it does not contain proper bi-ideals. Mathematics Subject Classification: 06F99

The notions of (transitive) soft d-algebras, soft edge d-algebras, soft d-algebras, soft dideals, soft d-ideals, soft d-ideals, and d-idealistic (d-idealistic, or d-idealistic) soft dalgebras are introduced. Also, their related properties are surveyed. © 2008 Elsevier Ltd. All rights reserved.

A right ideal is a language L over an alphabet Σ that satisfies L = LΣ∗. We show that there exists a stream (sequence) (Rn | n > 3) of regular right ideal languages, where Rn has n left quotients and is most complex under the following measures of complexity: the state complexities of the left quotients, the number of atoms (intersections of complemented and uncomplemented left quotients), the ...

(Received) We study the Weyl closure Cl(L) = K(x)h@iL \ D for an operator L of the rst Weyl algebra D = Khx;@i. We give an algorithm to compute Cl(L) and we describe its initial ideal under the order ltration. Our main application is an algorithm for constructing a Jordan-HH older series for a holonomic D-module and a formula for its length. Using the closure, we also reproduce a result of Strr...

The concept of (∈,∈∨ q)-fuzzy h-ideals of hemirings is introduced and some characterizations are described. We show that a hemiring S is hhemiregular if and only if for any (∈,∈∨ q)-fuzzy right h-ideal F and (∈,∈∨ q)fuzzy left h-ideal G, F ◦0.5 G = F ∩0.5 G. Finally, the concept of implicationbased fuzzy h-ideals of hemirings is considered. 2010 Mathematics Subject Classification: 16Y60, 13E05,...

The aim of this study is to introduce the concept of intuitionistic fuzzy (left, right) hyperideal in intuitionistic fuzzy semihypergroup based on the concept of intuitionistic fuzzy space as a direct generalization of the concept of fuzzy ideals in fuzzy semigroups, through the new approach of fuzzy space introduced by Dib and fuzzy hypergroup introduced by Fathi. A relationship between the in...

This article investigates the soft-interior (se) and the soft-cover (sc) of operator ideals. These operations, and especially the first one, have been widely used before, but making their role explicit and analyzing their interplay with the arithmetic mean operations is essential for the study in [10] of the multiplicity of traces. Many classical ideals are “soft”, i.e., coincide with their sof...