A simple method is described, to prove some theorems for simple hyper K-algebras and to study positive implicative hyper K-ideals, weak (implicative ) hyper K-ideals in simple hyper K-algebras . Beside, some results on positive implicative and (weak) implicative simple hyper K-algebras are presented. Finally classification of simple hyper Kalgebras of order 4, which are satisfied in conditions ...

let a be a banach algebra and e be a banach a-bimodule then s = a  e, the l1-direct sum of a and e becomes a module extension banach algebra when equipped with the algebras product (a; x):(a′; x′) = (aa′; a:x′ + x:a′). in this paper, we investigate △-amenability for these banach algebras and we show that for discrete inverse semigroup s with the set of idempotents es, the module extension bana...

Certain non-tempered liftings from PGL(2) × PGL(2) to PGSp(4) are constructed using the theory of (local and global) theta lifts. The resulting representations on PGSp(4) are the Saito–Kurokawa representations. The lifting is shown to be functorial under certain reasonable assumptions on the local Langlands correspondence for PGSp(4).

This paper is the second of a two part series. In this Part, we prove, using the description of simples obtained in Part I, that the variety $mathbf{RDQDStSH_1}$ of regular dually quasi-De Morgan Stone semi-Heyting algebras of level 1 is the join of the variety generated by the twenty 3-element $mathbf{RDQDStSH_1}$-chains and the variety of dually quasi-De Morgan Boolean semi-Heyting algebras--...