In this paper, a new notion, called TM-algebra, which is a generalization of the idea of Q/BCH/BCI/BCK/BCC-algebra, is introduced. Some theorems discussed in Q-and BCK algebras are generalized. Definition of TM-algebra along with various propositions are stipulated and presented with their respective proofs. The relation between TM-algebra and other algebra has been investigated and detailed in...

in this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring r. these fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...

38 and the rich amount of interesting relationships between them, are now well-understood (e.g., Co83, Ma88]). We believe that free amalgamation, rational amalgamation and a further construction called \innnite amalgamation" (still to be investigated) reeect this role on the higher level of amalgamation constructions. Many of the results that we have obtained for free and rational amalgamation ...

the notion of vague ideals in pseudo mv-algebras is introduced,and several properties are investigated. conditions for a vague set to be avague ideal are provided. conditions for a vague ideal to be implicative aregiven. characterizations of (implicative, prime) vague ideals are discussed.the smallest vague ideal containing a given vague set is established. primeand implicative extension proper...

‎in this paper‎, ‎we introduce the notion of the radical of a $pmv$-algebra $a$ and we charactrize radical $a$ via elements of $a$‎. ‎also‎, ‎we introduce the notion of the radical of a $cdot$-ideal in $pmv$-algebras‎. ‎several characterizations of this radical is given‎. ‎we define the notion of a semimaximal $cdot$-ideal in a $pmv$-algebra‎. ‎finally we show that $a/i$ has no nilpotent elemen...

The aim of this paper is to introduce the notions of ($epsilon, epsilon vee q$)-fuzzy p-ideals, ($epsilon, epsilon vee q$)-fuzzy q-ideals and ($epsilon, epsilon vee q$)-fuzzy a-ideals in BCIalgebras and to investigate some of their properties. Several characterizationtheorems for these generalized fuzzy ideals are proved and the relationshipamong these generalized fuzzy ideals of BCI-algebras i...

Let A be a Banach algebra and X be a Banach A-bimodule. In this paper, we define a new product on $Aoplus X$ and generalize the module extension Banach algebras. We  obtain characterizations of Arens regularity, commutativity, semisimplity, and study the ideal structure and derivations of this new Banach algebra.