Subvarieties of the variety of meadows
Jan A. Bergstra, Inge Bethke
TL;DR
This paper investigates subvarieties of meadows, which are commutative rings with a total inversion, by extending their axioms and expanding their signatures to better understand their algebraic structure.
Contribution
It introduces new subvarieties of meadows through extended axioms and signatures, advancing the algebraic theory of these structures.
Findings
Identification of new subvarieties within the meadow variety
Extension of axioms leads to richer algebraic structures
Enhanced understanding of total inversion in commutative rings
Abstract
Meadows - commutative rings equipped with a total inversion operation - can be axiomatized by purely equational means. We study subvarieties of the variety of meadows obtained by extending the equational theory and expanding the signature.
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Taxonomy
TopicsAdvanced Algebra and Logic · semigroups and automata theory · Rough Sets and Fuzzy Logic