Primeness property for graded central polynomials of verbally prime algebras |
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Authors: | Diogo Diniz Claudemir Fidelis Bezerra Júnior |
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Institution: | Departamento de Matemática, UAME/CCT-UFCG, Avenida Aprígio Veloso 882, 58109-970 Campina Grande-PB, Brazil |
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Abstract: | Let F be an infinite field. The primeness property for central polynomials of was established by A. Regev, i.e., if the product of two polynomials in distinct variables is central then each factor is also central. In this paper we consider the analogous property for and determine, within the elementary gradings with commutative neutral component, the ones that satisfy this property, namely the crossed product gradings. Next we consider , where R admits a regular grading, with a grading such that is a homogeneous subalgebra and provide sufficient conditions – satisfied by with the trivial grading – to prove that has the primeness property if does. We also prove that the algebras satisfy this property for ordinary central polynomials. Hence we conclude that, over a field of characteristic zero, every verbally prime algebra has the primeness property. |
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Keywords: | 16R20 16W50 16R99 |
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