In this paper, we introduce the concepts of fuzzy ideals, fuzzy implicative ideals and fuzzy p-ideals in BF-algebras and investigate some of its properties.

The aim of this paper is to introduce $(L,M)$-fuzzy closurestructure where $L$ and $M$ are strictly two-sided, commutativequantales. Firstly, we define $(L,M)$-fuzzy closure spaces and getsome relations between $(L,M)$-double fuzzy topological spaces and$(L,M)$-fuzzy closure spaces. Then, we introduce initial$(L,M)$-fuzzy closure structures and we prove that the category$(L,M)$-{bf FC} of $(L,M...

The paper considers the role of quantale algebra nuclei in representation of quotients of quantale algebras, and in factorization of quantale algebra homomorphisms. The set of all nuclei on a given quantale algebra is endowed with the structure of quantale semi-algebra.

Based on the notion of $Q$-sup-lattices (a fuzzy counterpart of complete join-semilattices valuated in a commutative quantale), we present the concept of $Q$-sup-algebras -- $Q$-sup-lattices endowed with a collection of finitary operations compatible with the fuzzy joins. Similarly to the crisp case investigated in cite{zhang-laan}, we characterize their subalgebras and quotients, and following...

To my dearest friend Najla Ali We introduce and investigate flat semimodules and k-flat semimodules. We hope these concepts will have the same importance in semimodule theory as in the theory of rings and modules. 1. Introduction. We introduce the notion of flat and k-flat. In Section 2, we study the structure ensuing from these notions. Proposition 2.4 asserts that V is flat if and only if (V ...

Let C → S be a proper flat family of stable curves, smooth over S0 = S r ∆. One can associate a flat family f : SUC(r, d) → S0 of moduli spaces SUCs(r, d) of semistable vector bundles of rank r and degree d with fixed determinant over the curves Cs, and also a line bundle Θ on SUC(r.d) such that its restriction to each fibre is the line bundle on SUCs(r, d) defined by the theta divisors. It is ...

Let R be a regular local ring, K its field of fractions and (V, φ) a quadratic space over R. In the case of R containing a field of characteristic zero we show that if (V, φ)⊗R K is isotropic over K, then (V, φ) is isotropic over R. 1 Characteristic zero case 1.0.1 Theorem (Main). Let R be a regular local ring, K its field of fractions and (V, φ) a quadratic space over R. Suppose R contains a f...