In this paper, the concepts of intuitionistic fuzzy translation to intuitionistic fuzzy Hideals in BCK/BCI-algebras are introduced. The notion of intuitionistic fuzzy extensions and intuitionistic fuzzy multiplications of intuitionistic fuzzy H-ideals with several related properties are investigated. Also the relationships between intuitionistic fuzzy translations, intuitionistic fuzzy extensio...

The notions of t-fuzzy left h-ideals, finite valued tfuzzy left h-ideals in a Γ−hemiring are introduced and some of their basic properties are investigated. t-fuzzy relations on a Γ−hemiring S are discussed and a characterization is given. Copyright c © 2011 Yang’s Scientific Research Institute, LLC. All rights reserved.

For countably generated ideals, J , of B(H), geometric stability is necessary for the canonical spectral characterization of sums of (J , B(H))–commutators to hold. This answers a question raised by Dykema, Figiel, Weiss and Wodzicki. There are some ideals, J , having quasi–nilpotent elements that are not sums of (J , B(H))–commutators. Also, every trace on every geometrically stable ideal is a...

For every prime integer p, M. Hochster conjectured the existence of certain p-torsion elements in a local cohomology module over a regular ring of mixed characteristic. We show that Hochster’s conjecture is false. We next construct an example where a local cohomology module over a hypersurface has p-torsion elements for every prime integer p, and consequently has infinitely many associated prim...

The aim of this article is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, we introduce the concepts of soft union hemirings (soft union h-ideals) of hemirings by soft intersection-union product and obtain some related results. Finally, we investigate some characterizations of h...

For countably generated ideals, J , of B(H), geometric stability is necessary for the canonical spectral characterization of sums of (J ; B(H)){commutators to hold. This answers a question raised by Dykema, Figiel, Weiss and Wodzicki. There are some ideals, J , having quasi{nilpotent elements that are not sums of (J ; B(H)){commutators. Also, every trace on every geometrically stable ideal is a...

The concepts of fuzzy semi-ideals of R with respect to H≤R and generalized fuzzy quotient rings are introduced. Some properties of fuzzy semiideals are discussed. Finally, several isomorphism theorems for generalized fuzzy quotient rings are established.

generalizing the concepts of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and   -fuzzy bi (generalized bi-) ideals in ternary semigroups, the notions of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and -fuzzy bi (generalized bi-) in ternary semigroups are introduced and several related properties are investigated. some new results are obtained.

In this paper, we describe the primitive ideal space of the $C^*$-algebra $C^*(mathcal G)$  associated to the ultragraph $mathcal{G}$. We investigate the structure of the closed ideals of the quotient ultragraph $  C^* $-algebra  $C^*left(mathcal G/(H,S)right)$ which contain no nonzero set projections and then we characterize all non gauge-invariant primitive ideals. Our results generalize the ...