In this note, we show that there is no Hopf algebra structure onQ∞, the algebra of pseudo-roots of noncommutative polynomials, which extends the one existing on NSym (one of its famous subalgebras).

The concept of soft translations of soft subalgebras and soft ideals over BCI/BCK-algebras is introduced and some related properties are studied. Notions of Soft extensions of soft subalgebras and soft ideals over BCI/BCK-algebras are also initiated. Relationships between soft translations and soft extensions are explored.

In this note, we show that there is no Hopf algebra structure onQ∞, the algebra of pseudo-roots of noncommutative polynomials, which extends the one existing on NSym (one of its famous subalgebras).

We consider 3-Jordan algebras, i.e., the nonassociative commutative algebras satisfying (x^3 y)x=x^3(yx). The variety of 3-Jordan algebras contains all Jordan algebras and all pseudo-composition algebras. We prove that a simple 3-Jordan algebra with idempotent is either a Jordan algebra or a pseudo-composition algebra. Disciplines Algebra | Mathematics Comments This article is published as Hent...

Abstract This paper introduces the idea of £-Smarandache pseudo fuzzy ideal a BH–algebra. Some suggestions and examples are given to comprehend features this decide connected aspects among them with

In this paper by considering the notion of BCK-module X, we introduce new concept which is named extended BCK-module or briefly X-module and we obtain some interesting results by it. Furthermore, we define the notion of multiplication X-module. 2000 Mathematics subject classification: 06D99 • 08A30