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6.816  Articles
1 of 683 pages  |  10  records  |  more records»
In this paper we study on division algorithm and Gröbner bases in the multivariate quaternionic polynomial ring.

In this paper we study on division algorithm and Gröbner bases in the multivariate quaternionic polynomial ring.

Over any field an implicit linear difference equation one can reduce to the usual explicit one, which has infinitely many solutions ~ one for each initial value. It is interesting to consider an implicit difference equation over any ring, because the case... see more

A Ringel ladder can be formed by a self-bar-amalgamation operation on a symmetric ladder, that is, by joining the root vertices on its end-rungs. The present authors have previously derived criteria under which linear chains of copies of one or more graph... see more

A ring  can be formed into a new ring, called a polynomial ring or what is often called an  ring. For  is a polynomial ring which is often referred to as an integer polynomial ring modulo n. The polynomial ring of R is the set of all polyno... see more

In this article, we carry out the investigation for regular sequences of symmetric polynomials in the polynomial ring in three and four variable. Any two power sum element in C[x_1, x_2, . . . , x_n] for n = 3 always form a regular sequence and we state t... see more

We study the commutativity of certain class of rings, namely rings with unity 1 and right s-unital under each of the following properties [yxm - xn f (y) xP, x]= 0, [yxm + xn f (y) xP, x] = 0, where f (t) is a polynomial in t2Z [t] varying with pair of ri... see more

This article continues the exploration of methods based on that of Gian-Carlo Rota that involve apolar invariants used for solving cubic and quintic polynomial equations. These polynomial invariants were disclosed previously as an alternative to and to cl... see more

Let R be any ring with identity 1, s be an endomorphism and d be a left s-derivation. In this paper, we will investigate the centre of some skew polynomial rings in the case when R is a commutative domain and s is anautomorphism. More precisely, let D be ... see more

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