In this paper, the concept of Semi-group in multiset context is introduced. The condition for a sub semi-multigroup to be established and study closure operationson class finite semi-multigroups carried out.Commutative andcancellative properties operations on are studied. We also studiedthe commutative cancellative semi-multigroups.

Let $D$ be an integral domain and $\Gamma$ a torsion-free commutative cancellative (additive) semigroup with identity element quotient group $G$. In this paper, we show that if char$(D)=0$ (resp., char$(D)=p>0$), then $D[\Gamma]$ is weakly Krull only UMT-domain, UMT-monoid, $G$ of type $(0,0,0, \dots )$ except $p$). Moreover, give arithmetical applications result.

In this work we solve an open problem of U.Höhle ([10], Problem 11). We show that the solution gives a characterization of all conditionally cancellative t-subnorms. Further, we give an equivalence condition for a conditionally cancellativite t-subnorm to be a t-norm and hence show that conditionally cancellativite t-subnorms whose natural negations are strong are, in fact, t-norms. Mathematics...

ΠMTL is a schematic extension of the monoidal t-norm based logic (MTL) by the characteristic axioms of product logic. In this paper we prove that ΠMTL satisfies the standard completeness theorem. From the algebraic point of view, we show that the class of ΠMTL-algebras (bounded commutative cancellative residuated l-monoids) in the real unit interval [0, 1] generates the variety of all ΠMTL-alge...

We give characterizations of the property of being weakly reductive for finitely generated commutative semigroups. As a consequence of these characterizations we obtain an algorithm for determining from a presentation of a finitely generated commutative semigroup whether it is weakly reductive. Furthermore, we present some connections between cancellative finitely generated commutative semigrou...

In this work we solve an open problem of U.Höhle [Problem 11, Fuzzy Sets and Systems 145 (2004) 471-479]. We show that the solution gives a characterization of all conditionally cancellative t-subnorms. Further, we give an equivalence condition for a conditionally cancellativite t-subnorm to be a t-norm and hence show that conditionally cancellativite t-subnorms whose natural negations are stro...