On Finite Basis Property for Joins of Varieties of Associative Rings |
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Authors: | Nikolay Silkin |
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Institution: | 1. Department of Mathematics , University of Northern Iowa , Cedar Falls, Iowa, USA silkin@math.uni.edu |
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Abstract: | If all finitely generated rings in a variety of associative rings satisfy the ascending chain condition on two-sided ideals, the variety is called locally weak noetherian. If there is an upper bound on nilpotency indices of nilpotent rings in a variety, the variety is called a finite index variety. We prove that the join of a finitely based locally weak noetherian variety and a variety of finite index is also finitely based and locally weak noetherian. One consequence of this result is that if an associative ring variety is connected by a finite path in the lattice of all associative ring varieties to a finitely based locally weak noetherian variety then such variety is also finitely based and locally weak noetherian. |
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Keywords: | Finite basis of identities Locally weak noetherian variety Polynomial identity Variety of associative rings |
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