Every Shift Automorphism Variety Has an Infinite Subdirectly Irreducible Member
نویسندگان
چکیده
A shift automorphism algebra is one satisfying the conditions of the shift automorphism theorem, and a shift automorphism variety is a variety generated by a shift automorphism algebra. In this paper, we show that every shift automorphism variety contains a countably infinite subdirectly irreducible algebra. 2000 Mathematics subject classification: primary 03C05; secondary 08B05, 08B26.
منابع مشابه
Two Finitely Generated Varieties Having No Infinite Simple Members
Using a method of R. McKenzie, we construct a finitely generated semisimple variety of infinite type, and a finitely generated nonsemisimple variety of finite type, both having arbitrarily large finite but no infinite simple members. This amplifies M. Valeriote’s negative solution to Problem 11 from [1]. R. McKenzie [2] has constructed a finitely generated variety having arbitrarily large finit...
متن کاملSubdirectly irreducible semilattices with an automorphism
In other words, SA is the variety of semilattices with one automorphism (which is, as well as its inverse, considered as an additional fundamental operation). The aim of this paper is to find all subdirectly irreducible algebras in SA . A universal algebra A is said to be subdirectly irreducible (shortly, an SI algebra) if it contains more than one element and among all the nontrivial congruenc...
متن کاملMaximal n-generated subdirect products
For n a positive integer and K a finite set of finite algebras, let L(n,K) denote the largest n-generated subdirect product whose subdirect factors are algebras in K. When K is the set of all ngenerated subdirectly irreducible algebras in a locally finite variety V, then L(n,K) is the free algebra FV(n) on n free generators for V. For a finite algebra A the algebra L(n, {A}) is the largest n-ge...
متن کاملRepresentable Idempotent Commutative Residuated Lattices
It is proved that the variety of representable idempotent commutative residuated lattices is locally finite. The n-generated subdirectly irreducible algebras in this variety are shown to have at most 3n+1 elements each. A constructive characterization of the subdirectly irreducible algebras is provided, with some applications. The main result implies that every finitely based extension of posit...
متن کاملOn the Loewy Rank of Infinite Algebras
The Loewy rank of a complete lattice L is deened as follows. Take the meet a 1 of all coatoms of L. Then let a 2 be the meet of all lower covers of a 1. Iterate this process to deene a for every ordinal by letting a +1 be the meet of all lower covers of a , and a the meet of all a (for <) if is a limit ordinal. The Loewy rank of L is the smallest ordinal for which a is the zero of L, and the sy...
متن کامل