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Direct products, varieties, and compactness conditions. (English) Zbl 1401.08003
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
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##### References:
 [1] G. Baumslag, A. Myasnikov and V. Roman’kov, Two theorems about equationally Noetherian groups, J. Algebra 194 (1997), no. 2, 654-664. · Zbl 0888.20017 [2] E. Daniyarova, A. Myasnikov and V. Remeslennikov, Unification theorems in algebraic geometry, Aspects of Infinite Groups, Algebra Discrete Math. 1, World Science Publisher, Hackensack (2008), 80-111. · Zbl 1330.08003 [3] E. Daniyarova, V. Remeslennikov and A. Myasnikov, Algebraic geometry over algebraic structures III: Equationally Noetherian property and compactness, Southeast Asian Bull. Math. 35 (2011), no. 1, 35-68. · Zbl 1240.08002 [4] E. Y. Daniyarova, A. G. Myasnikov and V. N. Remeslennikov, Algebraic geometry over algebraic systems. II. Foundations, Fundam. Prikl. Mat. 17 (2011/12), no. 1, 65-106. [5] P. Modabberi and M. Shahryari, Compactness conditions in universal algebraic geometry, Algebra Logic 55 (2016), no. 2, 146-172. · Zbl 1367.08002 [6] B. I. Plotkin, Problems in algebra inspired by universal algebraic geometry, Fundam. Prikl. Mat. 10 (2004), no. 3, 181-197. · Zbl 1072.08002
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