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Structure of relatively free dimonoids. (English) Zbl 1371.08006

A dimonoid is an algebra with two associative operations \(\vdash\), \(\dashv\) and with an identity \((x\vdash y)\dashv z= x\vdash (y\dashv z)\). The paper presents constructions of free dimonoids in the cases where one of the operations is a left (right) zero semigroup, a rectangular band, a normal (left, right) band etc. Constructions of free nilpotent, dinilpotent, abelian and some others diminoids are given. These constructions present canonical form of elements.

MSC:

08B20 Free algebras
08A30 Subalgebras, congruence relations
20M10 General structure theory for semigroups
08A05 Structure theory of algebraic structures
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