Shahryari, Mohammad; Shevlyakov, Artem Direct products, varieties, and compactness conditions. (English) Zbl 1401.08003 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. Cited in 1 Document 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 PDF BibTeX XML Cite \textit{M. Shahryari} and \textit{A. Shevlyakov}, Groups Complex. Cryptol. 9, No. 2, 159--166 (2017; Zbl 1401.08003) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.