Affine Complete Algebras

AbstractThe main results of the paper are the following: 1. Every locally finite affine complete variety admits a near unanimity term; 2. A locally finite congruence distributive variety is affine complete if and only if all its algebras with no proper subalgebras are affine complete and the variety is generated by one of such algebras. The first of these results sharpens a result of McKenzie asserting that all locally finite affine complete varieties are congruence distributive. The second one generalizes the result by Kaarli and Pixley that characterizes arithmetical affine complete varieties.

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Affine complete varieties are congruence distributive

Algebra Universalis ◽

10.1007/s000120050058 ◽

1997 ◽

Vol 38 (3) ◽

pp. 329-354 ◽

Cited By ~ 3

Author(s):

K. Kaarli ◽

R. McKenzie

Keyword(s):

Affine Complete ◽

Congruence Distributive

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Arithmetical affine complete varieties and inverse monoids

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/sscmath.2007.1040 ◽

2008 ◽

Vol 45 (1) ◽

pp. 13-28 ◽

Cited By ~ 1

Author(s):

Kalle Kaarli

Keyword(s):

Distributive Lattice ◽

Finite Type ◽

Categorical Equivalence ◽

Inverse Monoids ◽

Affine Complete

This paper gives a classification of arithmetical affine complete varieties of finite type up to categorical equivalence. It is proved that two such varieties are equivalent as categories if and only if their weakly diagonal generators have isomorphic monoids of bicongruences. Moreover, it is proved that the monoids appearing in this situation are precisely the inverse factorizable monoids with zero, with distributive lattice of idempotents, and satisfying a certain idempotent-unit condition (IU).

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Divisor Class Groups of Affine Complete Intersections

Singularities and Computer Algebra ◽

10.1007/978-3-319-28829-1_7 ◽

2017 ◽

pp. 147-160

Author(s):

Helmut A. Hamm

Keyword(s):

Complete Intersections ◽

Class Groups ◽

Divisor Class ◽

Affine Complete

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