Given a topological group G, and a finitely generated group Γ, a homomorphism π : Γ→G is locally rigid if any nearby by homomorphism π′ is conjugate to π by a small element of G. In 1964, Weil gave a criterion for local rigidity of a homomorphism from a finitely generated group Γ to a finite dimensional Lie group G in terms of cohomology of Γ with coefficients in the Lie algebra of G. Here we g...

Given a topological group G, and a finitely generated group Γ, a homomorphism π : Γ→G is locally rigid if any nearby by homomorphism π is conjugate to π by a small element of G. In 1964, Weil gave a criterion for local rigidity of a homomorphism from a finitely generated group Γ to a finite dimensional Lie group G in terms of cohomology of Γ with coefficients in the Lie algebra of G. Here we ge...

Firstly, soft hyperideals of hyperlattices are introduced and several interesting examples of them are given. Secondly, fuzzy soft hyperideals are proposed, which are generalizations of hyperideals and soft hyperideals in hyperlattices. After that, equivalent conditions of fuzzy soft hyperideals are given by using level soft sets. Finally, under the fuzzy soft homomorphism of hyperlattices, the...

In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore,...

We proposed the theory of multi-fuzzy sets [Sabu and Ramakrishnan (2010a), (2011a)] as an extension of theories of fuzzy sets, L-fuzzy sets [Goguen (1967)] and intuitionistic fuzzy sets [Atanassov (1986)]. Theory of multi-fuzzy sets deals with multi-level fuzziness and multi-dimensional fuzziness. Our previous papers discussed the basic notions of multi-fuzzy sets, multi-fuzzy topology, and mul...

One of the main problems in FCA (especially in fuzzy setting) is to reduce a concept lattice to appropriate size to make it graspable and understandable. We generalize known results on the correspondence of block relations of formal contexts and complete tolerances on concept lattices to fuzzy setting. Using an illustrative example we show that the results can be used for reduction of fuzzy con...

Let p > 2 be a prime, The group ring RG is calculated nearly up to Morita equivalence: The projections of RG into the simple components of KG are given explicitly and the endomorphism rings and homomorphism bimodules between the projective indecomposable RG-lattices are described.

It is a known fact that the subobjects of an object in an adhesive category form a distributive lattice. Building on this observation, in the paper we show how the representation theorem for finite distributive lattices applies to subobject lattices. In particular, we introduce a notion of irreducible object in an adhesive category, and we prove that any finite object of an adhesive category ca...

We study the problem of representing a pair of algebraic lattices, L1 and L0, as Con(A1) and Con(A0), respectively, with A1 an algebra and A0 a subalgebra of A1, and we provide such a representation in a special case. Back in 1971, Ervin Fried posed the problem of representing a pair of algebraic lattices, L1 and L0, as Con(A1) and Con(A0), respectively, with A1 an algebra and A0 a subalgebra o...

In this note, by considering the notions of the intuitionistic general L-fuzzy automaton and $(alpha, beta)$-language, we show that for any $(alpha, beta)$-language $mathcal{L}$, there exists a minimal intuitionistic general L-fuzzy automaton recognizing $mathcal{L}$.We prove that the minimal intuitionistic general L-fuzzy automaton is isomorphic with threshold $(alpha,beta)$ to any $(alpha, be...