We propose an operadic framework suitable for describing algebraic structures with operations being multilinear differential operators of varying orders or, more generally, formal series such operators. The is built upon the notion a multifiltration linear operad generalizing concept filtration associative algebra. describe particular way constructing and analyzing multifiltrations based on pre...

Pseudo-linear algebra is the study of common properties of linear differential and difference operators. We introduce in this paper its basic objects (pseudo-derivations, skew polynomials, and pseudo-linear operators) and describe several recent algorithms on them, which, when applied in the differential and difference cases, yield algorithms for uncoupling and solving systems of linear differe...

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).

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).

Recently, Zharkov and Blinkov introduced the notion of involutive bases of polynomial ideals. This involutive approach has its origin in the theory of partial di erential equations and is a translation of results of Janet and Pommaret. In this paper we present a pure algebraic foundation of involutive bases of Pommaret type. In fact, they turn out to be generalized left Grobner bases of ideals...

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 we generalize the involutive methods and algorithms devised for polynomial ideals to differential ones generated by a finite set of linear differential polynomials in the differential polynomial ring over a zero characteristic differential field. Given a ranking of derivative terms and an involutive division, we formulate the involutivity conditions which form a basis of involutiv...