The aim of this paper is to extend the truth value table oflattice-valued convergence spaces to a more general case andthen to use it to introduce and study the quantale-valued fuzzy Scotttopology in fuzzy domain theory. Let $(L,*,varepsilon)$ be acommutative unital quantale and let $otimes$ be a binary operationon $L$ which is distributive over nonempty subsets. The quadruple$(L,*,otimes,varep...

and the norm of an element is defined by ||/|| = ƒ | f(t) \ dt. In [4] Rudin showed that every function in L(R) is the convolution of two other functions. In other words, every element of the convolution algebra L(R) can be factored in L 1 ^ )» although this algebra lacks a unit. Subsequently, Cohen [ l ] observed that the essential ingredient in Rudin's argument is that ^(R) has an approximate...

Let G be a group, F a field of prime characteristic p and V a finite-dimensional FGmodule. Let L(V ) denote the free Lie algebra on V regarded as an FG-submodule of the free associative algebra (or tensor algebra) T (V ). For each positive integer r, let Lr(V ) and T r(V ) be the rth homogeneous components of L(V ) and T (V ), respectively. Here Lr(V ) is called the rth Lie power of V . Our mai...

In this paper, we apply the concept of an interval-valued intuitionistic fuzzy set to ideals and closed ideals in BG-algebras. The notion of an interval-valued intuitionistic fuzzy closed ideal of a BG-algebra is introduced, and some related properties are investigated. Also, the product of interval-valued inntuitionistic fuzzy BG-algebra is investgated.

Based on a complete Heyting algebra, we modify the definition of lattice-valued fuzzifying convergence space using fuzzy inclusion order and construct in this way a Cartesian-closed category, called the category of L−ordered fuzzifying convergence spaces, in which the category of L−fuzzifying topological spaces can be embedded. In addition, two new categories are introduced, which are called th...

By generalizing the method used by Tignol and Amitsur in [TA85], we determine necessary and sufficient conditions for an arbitrary tame central division algebra D over a Henselian valued field E to have Kummer subfields [Corollary 2.11 and Corollary 2.12]. We prove also that if D is a tame semiramified division algebra of prime power degree p over E such that p 6= char(Ē) and rk(ΓD/ΓF ) ≥ 3 [re...

Sheaves of structures are useful to give constructions in universal algebra and model theory. We can describe their logical behavior terms Heyting-valued structures. In this paper, we first provide a systematic treatment sheaves from the viewpoint categorical logic. then prove form {\L}o\'s's theorem for also characterization which holds with respect any maximal filter.

A rather simple natural outer derivation of the graded Lie algebra of all vector valued differential forms with the Frölicher-Nijenhuis bracket turns out to be a differential and gives rise to a cohomology of the manifold, which is functorial under local diffeomorphisms. This cohomology is determined as the direct product of the de Rham cohomology space and the graded Lie algebra of ”traceless”...

Let $mathfrak{L}$ be the Virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. We investigate the structure of the Lie triplederivation algebra of $mathfrak{L}$ and $mathfrak{g}$. We provethat they are both isomorphic to $mathfrak{L}$, which provides twoexamples of invariance under triple derivation.