Displaying similar documents to “Z2-Graded Polynomial Identities for Superalgebras of Block-Triangular Matrices”

A Basis for Z-Graded Identities of Matrices over Infinite Fields

Azevedo, Sergio (2003)

Serdica Mathematical Journal

Similarity:

2000 Mathematics Subject Classification: 16R10, 16R20, 16R50 The algebra Mn(K) of the matrices n × n over a field K can be regarded as a Z-graded algebra. In this paper, it is proved that if K is an infinite field, all the Z-graded polynomial identities of Mn(K) follow from the identities: x = 0, |α(x)| ≥ n, xy = yx, α(x) = α(y) = 0, xyz = zyx, α(x) = −α(y) = α(z ), where α is the degree of the corresponding variable. This is a generalization of a result of Vasilovsky about...

On Ordinary and Z2-graded Polynomial Identities of the Grassmann Algebra

Ribeiro Tomaz da Silva, Viviane (2012)

Serdica Mathematical Journal

Similarity:

2010 Mathematics Subject Classification: Primary: 16R10, Secondary: 16W55. The main purpose of this paper is to provide a survey of results concerning the ordinary and Z2-graded polynomial identities of the infinite dimensional Grassmann algebra over a field of characteristic zero, as well as of its sequences of ordinary and Z2-graded codimensions and cocharacters. We also intend to describe briefly the techniques used by the authors in order to illustrate some important...

Gradings and Graded Identities for the Matrix Algebra of Order Two in Characteristic 2

Koshlukov, Plamen, César dos Reis, Júlio (2012)

Serdica Mathematical Journal

Similarity:

2010 Mathematics Subject Classification: 16R10, 16R99, 16W50. Let K be an infinite field and let M2(K) be the matrix algebra of order two over K. The polynomial identities of M2(K) are known whenever the characteristic of K is different from 2. The algebra M2(K) admits a natural grading by the cyclic group of order 2; the graded identities for this grading are known as well. But M2(K) admits other gradings that depend on the field and on its characteristic. Here we describe...

A Basis for the Graded Identities of the Pair (M2(K), gl2(K))

Koshlukov, Plamen, Krasilnikov, Alexei (2012)

Serdica Mathematical Journal

Similarity:

2010 Mathematics Subject Classification: 16R10, 17B01. Let M2(K) be the algebra of 2×2 matrices over an infinite integral domain K. In this note we describe a basis for the Z2-graded identities of the pair (M2(K),gl2(K)). ∗ Partially supported by CNPq (Grant 304003/2011-5) and FAPESP (Grant 2010/50347-9). ∗∗ Partially supported by CNPq, DPP/UnB and by CNPq-FAPDF PRONEX grant 2009/00091-0 (193.000.580/2009).

Some properties of graded comultiplication modules

Khaldoun Al-Zoubi, Amani Al-Qderat (2017)

Open Mathematics

Similarity:

Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper we will obtain some results concerning the graded comultiplication modules over a commutative graded ring.