Direct products, varieties, and compactness conditions. (English) Zbl 1401.08003

Shahryari, Mohammad; Shevlyakov, Artem

Groups Complex. Cryptol. 9, No. 2, 159-166 (2017).

Summary: We study equationally Noetherian and \(\mathbf{q}_{\omega}\)-compact varieties of groups, rings and monoids. Moreover, we describe equationally Noetherian direct powers for these algebraic structures.

MSC:

08B25	Products, amalgamated products, and other kinds of limits and colimits
08A45	Equational compactness
03C05	Equational classes, universal algebra in model theory
14A99	Foundations of algebraic geometry

Keywords:

direct products; varieties; equationally Noetherian property

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