Maltsev conditions and relations on algebras

1999 ◽  
Vol 42 (4) ◽  
pp. 299-309 ◽  
Author(s):  
J.W. Snow
Keyword(s):  
Maltsev Conditions

Simpler Maltsev conditions for (weak) difference terms in locally finite varieties

2017 ◽  
Vol 78 (4) ◽  
pp. 555-561 ◽  
Author(s):  
Keith A. Kearnes ◽  
Ágnes Szendrei ◽  
Ross Willard
Keyword(s):  
Locally Finite ◽  
Maltsev Conditions ◽  
Locally Finite Varieties

scholarly journals Hardness results for the subpower membership problem

2018 ◽  
Vol 28 (05) ◽  
pp. 719-732
Author(s):  
Jeff Shriner
Keyword(s):  
Finite Algebra ◽  
Membership Problem ◽  
Finite Algebras ◽  
Maltsev Condition ◽  
Cube Term ◽  
Maltsev Conditions ◽  
Congruence Distributive

The main result of this paper shows that if [Formula: see text] is a consistent strong linear Maltsev condition which does not imply the existence of a cube term, then for any finite algebra [Formula: see text] there exists a new finite algebra [Formula: see text] which satisfies the Maltsev condition [Formula: see text], and whose subpower membership problem is at least as hard as the subpower membership problem for [Formula: see text]. We characterize consistent strong linear Maltsev conditions which do not imply the existence of a cube term, and show that there are finite algebras in varieties that are congruence distributive and congruence [Formula: see text]-permutable ([Formula: see text]) whose subpower membership problem is EXPTIME-complete.

scholarly journals ON THE COMPLEXITY OF SOME MALTSEV CONDITIONS

2009 ◽  
Vol 19 (01) ◽  
pp. 41-77 ◽  
Author(s):  
RALPH FREESE ◽  
MATTHEW A. VALERIOTE
Keyword(s):  
Polynomial Time ◽  
Finite Algebra ◽  
Free Algebras ◽  
Congruence Distributivity ◽  
Sharp Bounds ◽  
Polynomial Time Algorithms ◽  
Maltsev Conditions

This paper studies the complexity of determining if a finite algebra generates a variety that satisfies various Maltsev conditions, such as congruence distributivity or modularity. For idempotent algebras we show that there are polynomial time algorithms to test for these conditions but that in general these problems are EXPTIME complete. In addition, we provide sharp bounds in terms of the size of two-generated free algebras on the number of terms needed to witness various Maltsev conditions, such as congruence distributivity.

scholarly journals Characterizations of several Maltsev conditions

2015 ◽  
Vol 73 (3-4) ◽  
pp. 205-224 ◽  
Author(s):  
Marcin Kozik ◽  
Andrei Krokhin ◽  
Matt Valeriote ◽  
Ross Willard
Keyword(s):  
Maltsev Conditions

scholarly journals Random models of idempotent linear Maltsev conditions. I. Idemprimality

2020 ◽  
Vol 81 (1) ◽  
Author(s):  
Clifford Bergman ◽  
Ágnes Szendrei
Keyword(s):  
Random Models ◽  
Maltsev Conditions
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