Let us consider the algebra H-B-M , where is a distributive lattice, is a H-algebra (Heyting algebra), is a B-algebra (Brouwer algebra), < A, 0, 1,∨,∧,⇒, −̇ > is HB-algebra (semi-Boolean algebra) [10], is a de Morgan algebra, < A, 0, 1,∨,∧,⇒,∼> is a symmetrical Heyting algebra [5] and, respectively is a symmetr...

let  be a banach algebra. let  be linear mappings on . first we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple banach algebras, in certain case. afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...

‎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 paper considers the role of quantale algebra nuclei in representation of quotients of quantale algebras, and in factorization of quantale algebra homomorphisms. The set of all nuclei on a given quantale algebra is endowed with the structure of quantale semi-algebra.