On finite basis property for joins of varieties of associative rings
Finite basis of identities, Locally weak noetherian variety, Polynomial identity, Variety of associative rings
Communications in Algebra
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. © Taylor & Francis Group, LLC.
Original Publication Date
DOI of published version
Silkin, Nikolay, "On finite basis property for joins of varieties of associative rings" (2010). Faculty Publications. 2051.