IDEMPOTENT n-PERMUTABLE VARIETIES

نویسنده

  • M. VALERIOTE
چکیده

One of the important classes of varieties identified in tame congruence theory is the class of varieties which are n-permutable for some n. In this paper we prove two results: (1) For every n > 1 there is a polynomial-time algorithm which, given a finite idempotent algebra A in a finite language, determines whether the variety generated by A is n-permutable; (2) A variety is n-permutable for some n if and only if it interprets an idempotent variety which is not interpretable in the variety of distributive lattices.

برای دانلود 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

Varieties Whose Tolerances Are Homomorphic Images of Their Congruences

The homomorphic image of a congruence is always a tolerance (relation) but, within a given variety, a tolerance is not necessarily obtained this way. By a Maltsev-like condition, we characterize varieties whose tolerances are homomorphic images of their congruences (TImC). As corollaries, we prove that the variety of semilattices, all varieties of lattices, and all varieties of unary algebras h...

متن کامل

QUASISHEFFER OPERATIONS AND k-PERMUTABLE ALGEBRAS

A well known theorem of Murskiı̆’s asserts that almost every finite, nonunary algebra is idemprimal. We derive an analagous result under the assumption that all basic operations are idempotent. If the algebra contains a basic l-ary idempotent operation with l > 2 then the algebra is idemprimal with probability 1. However, for an algebra with a single basic binary operation, the probability of id...

متن کامل

Single identities for varieties equivalent to quadruple systems

If H is a subgroup of the symmetric group $4, then a 3-groupoid (S, f ) is called H-permutable if f ( x ~ ( 1 ) , X a ( 2 ) , X ~ r ( 3 ) ) = X~(4) ~ f ( x l , x2 ,x3 ) = x4 for every cr C H. Some classes of generalized idempotent H-permutable 3-groupoids are equivalent to Steiner, Mendelsohn and other quadruple systems. We prove that the variety of generalized idempotent H-permutable 3-groupoi...

متن کامل

Principal and Syntactic Congruences in Congruence-distributive and Congruence-permutable Varieties

We give a new proof that a finitely generated congruence-distributive variety has finitely determined syntactic congruences (or equivalently, term finite principal congruences), and show that the same does not hold for finitely generated congruence-permutable varieties, even under the additional assumption that the variety is residually very finite. 2000 Mathematics subject classification: 08B10.

متن کامل

A CONGRUENCE IDENTITY SATISFIED BY m-PERMUTABLE VARIETIES

We present a new and useful congruence identity satisfied by m-permutable varieties. It has been proved in [L1] that every m-permutable variety satisfies a non-trivial lattice identity (depending only on m). In [L2] we have found another interesting identity: Theorem 1. For m ≥ 3, every m-permutable variety satisfies the congruence identity αβh = αγh, for h = m[ m+1 2 ]− 1 Here, [ ] denotes int...

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

برای دانلود 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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013