scholarly journals Every nearly idempotent plain algebra generates a minimal variety

1995 ◽  
Vol 34 (2) ◽  
pp. 322-325
Author(s):  
K. A. Kearnes
Keyword(s):  
Minimal Variety

scholarly journals Simple surjective algebras having no proper subalgebras

1990 ◽  
Vol 48 (3) ◽  
pp. 434-454 ◽  
Author(s):  
Ágnes Szendrei
Keyword(s):  
Subdirectly Irreducible ◽  
Irreducible Algebra ◽  
Minimal Variety ◽  
Locally Finite ◽  
Subdirectly Irreducible Algebra ◽  
Matrix Power

AbstractWe prove that every finite, simple, surjective algebra having no proper subalgebras is either quasiprimal or affine or isomorphic to an algebra term equivalent to a matrix power of a unary permutational algebra. Consequently, it generates a minimal variety if and only if it is quasiprimal. We show also that a locally finite, minimal variety omitting type 1 is minimal as a quasivariety if and only if it has a unique subdirectly irreducible algebra.

PERMUTATION IDENTITIES AND VARIETIES OF NILSEMIGROUPS

1993 ◽  
Vol 03 (02) ◽  
pp. 201-210
Author(s):  
XIAOYING YAN
Keyword(s):  
Equivalence Relation ◽  
Complete Lattice ◽  
Semigroup Variety ◽  
Infinite Subset ◽  
Equivalence Classes ◽  
Minimal Variety ◽  
Complete Sublattice ◽  
Countably Infinite ◽  
Semigroup Varieties

For any variety V of semigroups there exists a smallest semigroup variety PV containing V and closed for the construction of power semigroups. These varieties PV form a countably infinite subset PL(S) of the lattice L(S) of semigroup varieties. Though (PL(S), ⊆) is a complete lattice, it is not a complete sublattice of L(S). There exists however an interval in L(S) consisting of varieties of nilsemigroups which is isomorphic to (PL(S), ⊆). It will be shown that the equivalence classes of the equivalence relation induced by P: L(S)→PL(S), V↦PV, each contain a unique minimal variety consisting of nilsemigroups.

scholarly journals Symbolic Computation of the Orthogonal Projection of Rational Curves onto Rational Parameterized Surfaces

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Zhiwang Gan ◽  
Meng Zhou
Keyword(s):  
Symbolic Computation ◽  
Orthogonal Projection ◽  
Gröbner Basis ◽  
Rational Curves ◽  
Grobner Basis ◽  
Minimal Variety ◽  
The One ◽  
Symbolic Algorithms

This paper focuses on the orthogonal projection of rational curves onto rational parameterized surface. Three symbolic algorithms are developed and studied. One of them, based on regular systems, is able to compute the exact parametric loci of projection. The one based on Gröbner basis can compute the minimal variety that contains the parametric loci. The remaining one computes a variety that contains the parametric loci via resultant. Examples show that our algorithms are efficient and valuable.

scholarly journals An uncountable Jónsson algebra in a minimal variety

2019 ◽  
Vol 148 (4) ◽  
pp. 1765-1775
Author(s):  
Jordan DuBeau ◽  
Keith A. Kearnes
Keyword(s):  
Minimal Variety

Every idempotent plain algebra generates a minimal variety

1988 ◽  
Vol 25 (1) ◽  
pp. 36-39 ◽  
Author(s):  
�gnes Szendrei
Keyword(s):  
Minimal Variety

scholarly journals Minimal varieties and quasivarieties

1990 ◽  
Vol 48 (1) ◽  
pp. 133-147 ◽  
Author(s):  
Clifford Bergman ◽  
Ralph McKenzie
Keyword(s):  
Algebraic Logic ◽  
Deductive System ◽  
Sufficient Condition ◽  
Minimal Variety ◽  
Distributive Variety ◽  
Locally Finite ◽  
Congruence Distributive Variety ◽  
Simple Algebras ◽  
Congruence Distributive

AbstractWe prove that every locally finite, congruence modular, minimal variety is minimal as a quasivariety. We also construct all finite, strictly simple algebras generating a congruence distributive variety, such that the sett of unary term perations forms a group. Lastly, these results are applied to a problem in algebraic logic to give a sufficient condition for a deductive system to be structurally complete.

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