Commutator Theory for Relatively Modular Quasivarieties

نویسندگان

  • KEITH KEARNES
  • RALPH MCKENZIE
  • RALPH McKENZIE
چکیده

We develop a commutator theory for relatively modular quasivarieties that extends the theory for modular varieties. We characterize relatively modular quasivarieties, prove that they have an almost-equational axiomatization and we investigate the lattice of subquasivarieties. We derive the result that every finitely generated, relatively modular quasivariety of semigroups is finitely based.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Relatively Congruence Modular Quasivarieties of Modules

We show that the quasiequational theory of a relatively congruence modular quasivariety of left R-modules is determined by a two-sided ideal in R together with a filter of left ideals. The two-sided ideal encodes the identities that hold in the quasivariety, while the filter of left ideals encodes the quasiidentities. The filter of left ideals defines a generalized notion of torsion. It follows...

متن کامل

The Weak Extension Property and Finite Axiomatizability for Quasivarieties

We define and compare a selection of congruence properties of quasivarieties, including the relative congruence meet semi-distributivity, RSD(∧), and the weak extension property, WEP. We prove that if K ⊆ L ⊆ L′ are quasivarieties of finite signature, and L′ is finitely generated while K |= WEP, then K is finitely axiomatizable relative to L. We prove for any quasivariety K that K |= RSD(∧) iff...

متن کامل

Commutator Theory for Uniformities

We investigate commutator operations on compatible uniformities. We present a commutator operation for uniformities in the congruence-modular case which extends the commutator on congruences, and explore its properties. Introduction The purpose of this paper is to generalize the commutator of congruences to a commutator of compatible uniformities. Commutator theory (on congruences) works best f...

متن کامل

Commutator Theory for Compatible Uniformities

We investigate commutator operations on compatible uniformities. We define a commutator operation for uniformities in the congruence-modular case which extends the commutator on congruences, and explore its properties. Introduction The purpose of this paper is to generalize the commutator of congruences to a commutator of compatible uniformities. Commutator theory (on congruences) works best fo...

متن کامل

Commutator Theory for Loops

Using the Freese-McKenzie commutator theory for congruence modular varieties as the starting point, we develop commutator theory for the variety of loops. The fundamental theorem of congruence commutators for loops relates generators of the congruence commutator to generators of the total inner mapping group. We specialize the fundamental theorem into several varieties of loops, and also discus...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009