Displaying similar documents to “A note on normal varieties of monounary algebras”

k-Normalization and (k+1)-level inflation of varieties

Valerie Cheng, Shelly Wismath (2008)

Discussiones Mathematicae - General Algebra and Applications

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Let τ be a type of algebras. A common measurement of the complexity of terms of type τ is the depth of a term. For k ≥ 1, an identity s ≈ t of type τ is said to be k-normal (with respect to this depth complexity measurement) if either s = t or both s and t have depth ≥ k. A variety is called k-normal if all its identities are k-normal. Taking k = 1 with respect to the usual depth valuation of terms gives the well-known property of normality of identities or varieties. For any variety...

Some monounary algebras with EKP

Emília Halušková (2020)

Mathematica Bohemica

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An algebra 𝒜 is said to have the endomorphism kernel property (EKP) if every congruence on 𝒜 is the kernel of some endomorphism of 𝒜 . Three classes of monounary algebras are dealt with. For these classes, all monounary algebras with EKP are described.

The lattice of subvarieties of the biregularization of the variety of Boolean algebras

Jerzy Płonka (2001)

Discussiones Mathematicae - General Algebra and Applications

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Let τ: F → N be a type of algebras, where F is a set of fundamental operation symbols and N is the set of all positive integers. An identity φ ≈ ψ is called biregular if it has the same variables in each of it sides and it has the same fundamental operation symbols in each of it sides. For a variety V of type τ we denote by V b the biregularization of V, i.e. the variety of type τ defined by all biregular identities from Id(V). Let B be the variety of Boolean algebras of type τ b : + , · , ´ N , where...

A representation theorem for tense n × m -valued Łukasiewicz-Moisil algebras

Aldo Victorio Figallo, Gustavo Pelaitay (2015)

Mathematica Bohemica

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In 2000, Figallo and Sanza introduced n × m -valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of n -valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class n × m of tense n × m -valued Łukasiewicz-Moisil algebras (or tense LM n × m -algebras), namely n × m -valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense...

Bases for certain varieties of completely regular semigroups

Mario Petrich (2021)

Commentationes Mathematicae Universitatis Carolinae

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Completely regular semigroups equipped with the unary operation of inversion within their maximal subgroups form a variety, denoted by 𝒞ℛ . The lattice of subvarieties of 𝒞ℛ is denoted by ( 𝒞ℛ ) . For each variety in an -subsemilattice Γ of ( 𝒞ℛ ) , we construct at least one basis of identities, and for some important varieties, several. We single out certain remarkable types of bases of general interest. As an application for the local relation L , we construct 𝐋 -classes of all varieties in Γ . Two...

Transfer of derived equivalences from subalgebras to endomorphism algebras II

Shengyong Pan, Jiahui Yu (2024)

Czechoslovak Mathematical Journal

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We investigate derived equivalences between subalgebras of some Φ -Auslander-Yoneda algebras from a class of n -angles in weakly n -angulated categories. The derived equivalences are obtained by transferring subalgebras induced by n -angles to endomorphism algebras induced by approximation sequences. Then we extend our constructions in T. Brüstle, S. Y. Pan (2016) to n -angle cases. Finally, we give an explicit example to illustrate our result.