scholarly journals 2-Supernilpotent Mal’cev algebras

2013 ◽  
Vol 172 (2) ◽  
pp. 161-166 ◽  
Author(s):  
Nebojša Mudrinski
Keyword(s):  
Mal’Cev Algebras

Some applications of higher commutators in Mal’cev algebras

2010 ◽  
Vol 63 (4) ◽  
pp. 367-403 ◽  
Author(s):  
Erhard Aichinger ◽  
Nebojša Mudrinski
Keyword(s):  
Mal’Cev Algebras

A note on modularity in Mal'cev algebras

1988 ◽  
Vol 50 (5) ◽  
pp. 424-428 ◽  
Author(s):  
Alberto Elduque
Keyword(s):  
Mal’Cev Algebras

Mal'cev algebras satisfying Engel's condition

1975 ◽  
Vol 14 (4) ◽  
pp. 271-281 ◽  
Author(s):  
V. T. Filippov
Keyword(s):  
Mal’Cev Algebras

On semimodular Mal'cev algebras

1988 ◽  
Vol 50 (4) ◽  
pp. 328-336 ◽  
Author(s):  
Alberto Elduque
Keyword(s):  
Mal’Cev Algebras

Continuity of derivations on Mal'cev H*-algebras

1991 ◽  
Vol 110 (3) ◽  
pp. 455-459 ◽  
Author(s):  
Borut Zalar
Keyword(s):  
Lie Algebras ◽  
Jordan Algebras ◽  
Associative Algebras ◽  
Alternative Algebras ◽  
Mal’Cev Algebras ◽  
Long Time

A long time ago the concept of H*-algebra was introduced by Ambrose in [1] where the structure of complex associative H*-algebras was given. Since then this theory was extended to such classical types of non-associative algebras as alternative algebras (in [6]), Jordan algebras (in [5, 13, 14]), non-commutative Jordan algebras (in [5]), Lie algebras (in [3, 9, 10]) and Mal'cev algebras (in [2]).

scholarly journals SUPERNILPOTENCE PREVENTS DUALIZABILITY

2013 ◽  
Vol 96 (1) ◽  
pp. 1-24 ◽  
Author(s):  
WOLFRAM BENTZ ◽  
PETER MAYR
Keyword(s):  
Finite Type ◽  
Prime Power ◽  
Prime Power Order ◽  
Theoretic Approach ◽  
Direct Products ◽  
Group Operation ◽  
Infinite Type ◽  
Mal’Cev Algebras ◽  
Nilpotent Algebras ◽  
Curious Property

AbstractWe address the question of the dualizability of nilpotent Mal’cev algebras, showing that nilpotent finite Mal’cev algebras with a nonabelian supernilpotent congruence are inherently nondualizable. In particular, finite nilpotent nonabelian Mal’cev algebras of finite type are nondualizable if they are direct products of algebras of prime power order. We show that these results cannot be generalized to nilpotent algebras by giving an example of a group expansion of infinite type that is nilpotent and nonabelian, but dualizable. To our knowledge this is the first construction of a nonabelian nilpotent dualizable algebra. It has the curious property that all its nonabelian finitary reducts with group operation are nondualizable. We were able to prove dualizability by utilizing a new clone theoretic approach developed by Davey, Pitkethly, and Willard. Our results suggest that supernilpotence plays an important role in characterizing dualizability among Mal’cev algebras.

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