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Varieties of ordered algebras as categories
A variety is a category of ordered (finitary) algebras presented by inequations between terms. We characterize categories enriched over the category...
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Diagrammatic Presentations of Enriched Monads and Varieties for a Subcategory of Arities
The theory of presentations of enriched monads was developed by Kelly, Power, and Lack, following classic work of Lawvere, and has been generalized...
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Filter Classes of Upsets of Distributive Lattices
Let us say that a class of upward closed sets (upsets) of distributive lattices is a finitary filter class if it is closed under homomorphic...
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Appendix: Algebras of relations
In this chapter we briefly introduce the classes of algebras that have occurred in the book as algebraic versions of logics.1 This chapter is...
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The lattice of varieties of monoids
We survey results devoted to the lattice of varieties of monoids. Along with known results, some unpublished results are given with proofs. A number...
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Mal’tsev products of varieties, II
The Mal’tsev product of two varieties of the same similarity type is not in general a variety, because it can fail to be closed under homomorphic...
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Affine representability and decision procedures for commutativity theorems for rings and algebras
We consider applications of a finitary version of the Affine Representability theorem, which follows from recent work of Belov-Kanel, Rowen, and...
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Projectivity in (bounded) commutative integral residuated lattices
In this paper, we study projective algebras in varieties of (bounded) commutative integral residuated lattices. We make use of a well-established...
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Coextensive varieties via central elements
In this paper we use the theory of central elements in order to provide a characterization for coextensive varieties. In particular, if a variety is...
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On when the union of two algebraic sets is algebraic
In universal algebraic geometry, an algebra is called an equational domain if the union of two algebraic sets is algebraic. We characterize...
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Not all nilpotent monoids are finitely related
A finite semigroup is finitely related (has finite degree) if its term functions are determined by a finite set of finitary relations. For example,...
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Saturated free algebras and almost indiscernible theories
We extend the concept of “almost indiscernible theory” introduced by Pillay and Sklinos in 2015 (which was itself a modernization and expansion of...
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Equationally defined classes of semigroups
We apply, in the context of semigroups, the main theorem from the authors’ paper “Algebras defined by equations” (Higgins and Jackson in J Algebra...
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Filter pairs and natural extensions of logics
We adjust the notion of finitary filter pair, which was coined for creating and analyzing finitary logics, in such a way that we can treat logics of...
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Ind-Varieties of Generalized Flags: A Survey
This paper is a review of results on the structure of homogeneous ind-varieties G/P of the ind-groups G = GL ∞ (ℂ), SL ∞ (ℂ), SO ∞ (ℂ), and Sp ∞ (ℂ), subject...
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Splitting Borel Subalgebras of \(\mathfrak {sl} (\infty )\) , \(\mathfrak {o}(\infty )\) , \(\mathfrak {sp}(\infty )\) and Generalized Flags
Borel subalgebras play a prominent role in the representation theory of finite-dimensional Lie algebras and superalgebras, as well as of Kac–Moody...