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Left symmetric left distributive magmas and hypersubstitutions

Vanzurova A.

Demonstratio Mathematica

2006

Vol. 39, nr 3

491-506

Our aim is to generalize results reached in [A-D 98] and [V 04]. In [A-D 98], normal forms for terms with respect to the variety SIE of right symmetric idempotent entropic magmas are used to derive multiplication in the magma of normal form hypersubstitutions with respect to SIE, the monoid of SIE-proper normal form hypersubstitutions is found, and hyperidentities are discussed. In [V 04], a similar project is solved for the variety SID of left symmetric left distributive idempotent magmas (in which the variety dual to SIE is contained as a subvariety). Droppping idempotency we obtain a generalization, the variety SD of left symmetric left distributive magmas. We use again (naturally arising) normal forms for terms in SD to study the magma of SD-normal form hypersubstitutions, its multiplication (with six idempotents), and describe the monoid of SD-proper normal form hypersubstitutions. Comparison with the previous cases might be interesting.