Graded transcendental extensions of graded fields.
Boulagouaz, M. (2003)
International Journal of Mathematics and Mathematical Sciences
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Boulagouaz, M. (2003)
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Sands, A.D., Yahya, H. (2005)
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Azevedo, Sergio (2003)
Serdica Mathematical Journal
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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...
Tadeusz Józefiak (1976)
Fundamenta Mathematicae
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Khaldoun Al-Zoubi, Amani Al-Qderat (2017)
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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.
Koshlukov, Plamen, César dos Reis, Júlio (2012)
Serdica Mathematical Journal
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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...