Article in volume
Authors:
Title:
Algebraic geometry over complete lattices and involutive pocrims
PDFSource:
Discussiones Mathematicae - General Algebra and Applications 42(2) (2022) 339-347
Received: 2021-03-12 , Revised: 2021-04-06 , Accepted: 2022-05-20 , Available online: 2022-10-05 , https://doi.org/10.7151/dmgaa.1394
Abstract:
An involutive pocrim is a resituated integral partially ordered
commutative monoid with an involution operator, consider as an algebra. In this
paper it is proved that the variety of a finitely generated by involutive
pocrims of finite type has a finitely based equational theory. We also study the
algebraic geometry over compete lattices and we investigate the properties of
being equationally Noetherian and $u_\omega$-compact over such lattices.
Keywords:
congruence distributive, algebraically closed algebra, involutive pocrims, equationally Noetherian
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