Algebraic geometry over algebraic structures III: Equationally Noetherian property and compactness
arXiv:1002.4243
Abstract
In this paper we discuss some special generalizations of equationally Noetherian property which naturally arise in the universal algebraic geometry. We introduce weakly equationally Noetherian, qw-compact, uw-compact, and weakly uw-compact algebras and then examine properties of such algebras. Also we consider the connections between five classes: the class of equationally Noetherian algebras, the class of weakly equationally Noetherian algebras, the class of uw-compact algebras, the class of weakly uw-compact algebras, and the class of qw-compact algebras.
46 pages; 2 figures
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- Finite subsemigroups of free left regular bands
- Wreath products of semigroups in universal algebraic geometry and Plotkin's problem
- On the equationally Artinian groups
- Lectures notes in universal algebraic geometry
- On equations over direct powers of algebraic structures