Algebraic Geometry Over Algebraic Structures. IX. Principal Universal Classes and Dis-Limits

E. Y.U. Daniyarova, Alexei Miasnikov, V. N. Remeslennikov

Research output: Contribution to journalArticle

Abstract

This paper enters into a series of works on universal algebraic geometry—a branch of mathematics that is presently flourishing and is still undergoing active development. The theme and subject area of universal algebraic geometry have their origins in classical algebraic geometry over a field, while the language and almost the entire methodological apparatus belong to model theory and universal algebra. The focus of the paper is the problem of finding Dis-limits for a given algebraic structure A, i.e., algebraic structures in which all irreducible coordinate algebras over A are embedded and in which there are no other finitely generated substructures. Finding a solution to this problem necessitated a good description of principal universal classes and quasivarieties. The paper is divided into two parts. In the first part, we give criteria for a given universal class (or quasivariety) to be principal. In the second part, we formulate explicitly the problem of finding Dis-limits for algebraic structures and show how the results of the first part make it possible to solve this problem in many cases.

Original languageEnglish (US)
Pages (from-to)414-428
Number of pages15
JournalAlgebra and Logic
Volume57
Issue number6
DOIs
StatePublished - Jan 15 2019

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Algebraic Geometry
Algebraic Structure
Quasivariety
Universal Algebra
Model Theory
Substructure
Finitely Generated
Branch
Entire
Algebra
Series
Class

All Science Journal Classification (ASJC) codes

  • Analysis
  • Logic

Cite this

Daniyarova, E. Y.U. ; Miasnikov, Alexei ; Remeslennikov, V. N. / Algebraic Geometry Over Algebraic Structures. IX. Principal Universal Classes and Dis-Limits. In: Algebra and Logic. 2019 ; Vol. 57, No. 6. pp. 414-428.
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Algebraic Geometry Over Algebraic Structures. IX. Principal Universal Classes and Dis-Limits. / Daniyarova, E. Y.U.; Miasnikov, Alexei; Remeslennikov, V. N.

In: Algebra and Logic, Vol. 57, No. 6, 15.01.2019, p. 414-428.

Research output: Contribution to journalArticle

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