recently‎, ‎the authors gave some conditions under which a direct product‎ ‎of finitely many groups is $mathcal{v}-$capable if and only if each of its‎ ‎factors is $mathcal{v}-$capable for some varieties $mathcal{v}$‎. ‎in this paper‎, ‎we extend this fact to any infinite direct product of groups‎. ‎moreover‎, ‎we conclude some results for $mathcal{v}-$capability of direct products of infinitel...

The aim of this paper is the study of the sequence of join spacesand fuzzy subsets associated with a hypergroupoid. In thispaper we give some properties of the membership function$widetildemu_{otimes}$ corresponding to the direct pro-duct oftwo hypergroupoids and we determine the fuzzy grade of thehypergroupoid $langle Htimes H, otimesrangle$ in a particularcase.

This paper attempts to generalize universal algebras on classical sets to $L$-sets when $L$ is a GL-quantale. Some basic notions of fuzzy universal algebra on an $L$-set are introduced, such as subalgebra, quotient algebra, homomorphism, congruence, and direct product etc. The properties of them are studied. $L$-valued power algebra is also introduced and it is shown there is an onto homomorphi...

Using a t-norm T , the notion of T -fuzzy subhypernear-rings (for short TFSrings) of hypernear-rings is introduced and some of their properties are investigated. Also we study the structure of TFS-rings under direct product.

In the framework of fuzzy algebras with fuzzy equalities and acomplete lattice as a structure of membership values, we investigate fuzzyequational classes. They consist of special fuzzy algebras fullling the samefuzzy identities, dened with respect to fuzzy equalities. We introduce basicnotions and the corresponding operators of universal algebra: construction offuzzy subalgebras, homomorphisms...

bentea and tu{a}rnu{a}uceanu~(an. c{s}tiinc{t}. univ. al. i.cuza iac{s}, ser. nouv{a}, mat., {bf 54(1)} (2008), 209-220)proposed the following problem: find an explicit formula for thenumber of fuzzy subgroups of a finite hamiltonian group of type$q_8times mathbb{z}_n$ where $q_8$ is the quaternion group oforder $8$ and $n$ is an arbitrary odd integer. in this paper weconsider more general grou...

In this paper, the concept of (λ, μ)-hesitant fuzzy subalgebras is introduced in Boolean algebra. Some properties are discussed. Finally, we proved that intersection and direct product two also

An L-fuzzy generalization of the so-called Chu correspondences between formal contexts forms a category called L-ChuCors. In this work we show that this category naturally embeds ChuCors, and prove that it is *-autonomous. We also focus on the direct product of two L-fuzzy contexts, which is defined with the help of a binary operation, essentially a disjunction, on a lattice of truth-values L.