location:  Publications → journals
Search results

Search: All articles in the CJM digital archive with keyword tame congruence theory

 Expand all        Collapse all Results 1 - 2 of 2

1. CJM 2009 (vol 61 pp. 451)

Valeriote, Matthew A.
 A Subalgebra Intersection Property for Congruence Distributive Varieties We prove that if a finite algebra $\m a$ generates a congruence distributive variety, then the subalgebras of the powers of $\m a$ satisfy a certain kind of intersection property that fails for finite idempotent algebras that locally exhibit affine or unary behaviour. We demonstrate a connection between this property and the constraint satisfaction problem. Keywords:congruence distributive, constraint satisfaction problem, tame congruence theory, \jon terms, Mal'cev conditionCategories:08B10, 68Q25, 08B05

2. CJM 2002 (vol 54 pp. 736)

Kearnes, K. A.; Kiss, E. W.; Szendrei, Á.; Willard, R. D.
 Chief Factor Sizes in Finitely Generated Varieties Let $\mathbf{A}$ be a $k$-element algebra whose chief factor size is $c$. We show that if $\mathbf{B}$ is in the variety generated by $\mathbf{A}$, then any abelian chief factor of $\mathbf{B}$ that is not strongly abelian has size at most $c^{k-1}$. This solves Problem~5 of {\it The Structure of Finite Algebras}, by D.~Hobby and R.~McKenzie. We refine this bound to $c$ in the situation where the variety generated by $\mathbf{A}$ omits type $\mathbf{1}$. As a generalization, we bound the size of multitraces of types~$\mathbf{1}$, $\mathbf{2}$, and $\mathbf{3}$ by extending coordinatization theory. Finally, we exhibit some examples of bad behavior, even in varieties satisfying a congruence identity. Keywords:tame congruence theory, chief factor, multitraceCategory:08B26