Finite separability in varieties of associative rings

被引：0
作者：
Paison O.B.
Volkov M.V.
Sapir M.V.
机构：
来源：
Algebra and Logic | 1999年 / 38卷 / 2期
关键词：
Additive Group; Associative Algebra; Finite Index; Maximal Condition; Noetherian Ring;
D O I：
10.1007/BF02671724
中图分类号：
学科分类号：
摘要：
A subset M of a universal algebra A is called finitely separated in A if, for any element x ∈ A\M, there exists an homomorphism φ of A into a finite algebra, for which φ(x) ∉ φ(M). A ring is said to be S-separable (R-separable) if its subrings (resp., right ideals) are all finitely separated in it. We give equational (in the language of identities) and indicator (in the language of "prohibited" rings) characterizations of varieties consisting of S-separable (R-separable) rings. Moreover, varieties are described in which, not all, but finitely generated rings only share the properties mentioned. © 1999 Kluwer Academic/Plenum Publishers.
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页码：107 / 120
页数：13
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