the concept of right (left) quotient (or residual) of an ideal η by anideal ν of an l-subring μ of a ring r is introduced. the right (left) quotients areshown to be ideals of μ . it is proved that the right quotient [η :r ν ] of an idealη by an ideal ν of an l-subring μ is the largest ideal of μ such that[η :r ν ]ν ⊆ η . most of the results pertaining to the notion of quotients(or residual) of ...

A totally ordered monoid, or tomonoid for short, is a monoid endowed with a compatible total order. We deal in this paper with tomonoids that are finite and negative, where negativity means that the monoidal identity is the top element. Examples can be found, for instance, in the context of finite-valued fuzzy logic. By a Rees coextension of a negative tomonoid S, we mean a negative tomonoid T ...

Hypergroups can be subdivided into two large classes: those whose heart coincide with the entire hypergroup and in which is a proper sub-hypergroup. The latter class includes family of 1-hypergroups, reduces to singleton, therefore trivial group. However, very little known about hypergroups that are neither 1-hypergroups nor belong first class. goal this work take step classifying G-hypergroups...

The contribution aims to create hypergroups of linear first-order partial differential operators with proximities, one of which creates a tolerance semigroup on the power set of the mentioned differential operators. Constructions of investigated hypergroups are based on the so called “Ends-Lemma” applied on ordered groups of differnetial operators. Moreover, there is also obtained a regularly p...

Different partial hypergroupoids are associated with binary relations defined on a set H. In this paper we find sufficient and necessary conditions for these hypergroupoids in order to be reduced hypergroups. Given two binary relations and on H we investigate when the hypergroups associated with the relations ∩ , ∪ and are reduced. We also determine when the cartesian product of two hypergroupo...

In this paper, the new notions of ``belongingness ($in_{gamma}$)"and ``quasi-coincidence ($q_delta$)"  of a fuzzy point with a fuzzyset are  introduced. By means of this new idea, the  concept of$(alpha,beta)$-fuzzy $n$-ary subhypergroup of an $n$-aryhypergroup is given, where $alpha,betain{in_{gamma}, q_{delta},in_{gamma}wedge q_{delta}, ivq}$,  andit is shown that, in 16 kinds of $(alpha,beta...

In the elementary case of finitely many events, we generalise to Gödel (propositional infinite-valued) logic — one of the fundamental fuzzy logics in the sense of Hájek — the classical correspondence between partitions, quotient measure spaces, and push-forward measures. To achieve this end, appropriate Gödelian analogues of the Boolean notions of probability assignment and partition are needed...

The study of perfect, local and bipartite IMTL-algebras presented in [29] is generalized in this paper to the general non-involutive case, i. e. to MTL-algebras. To this end we describe the radical of MTL-algebras and characterize perfect MTL-algebras as those for which the quotient by the radical is isomorphic to the two-element Boolean algebra, and a special class of bipartite MTL-algebras, B...

Let K be a (commutative) locally compact hypergroup with a left Haar measure. Let L1(K) be the hypergroup algebra of K and UCl(K) be the Banach space of bounded left uniformly continuous complex-valued functions on K. In this paper we show, among other things, that the topological (algebraic) center of the Banach algebra UCl(K)* is M(K), the measure algebra of K.