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Embedding into almost left factorizable restriction semigroups. (English) Zbl 1275.20064
An algebra $$(S,\cdot,+,*)$$ of type $$(2,1,1)$$ is called a restriction semigroup if $$(S,\cdot)$$ is a semigroup, $$(S,\cdot,+)$$ satisfies the identities $$x^+x=x$$, $$x^+y^+=y^+x^+$$, $$(x^+y^+)^+=x^+y^+$$, $$xy^+=(xy)^+x$$, $$(S,\cdot,*)$$ satisfies the dual identities, and $$(x^+)^*=x^+$$, $$(x^*)^+=x^*$$.
The main result is Theorem 4.1. Each restriction semigroup is $$(2,1,1)$$-embeddable into an almost left factorizable restriction semigroup.
The definition of an almost left factorizable restriction semigroup is too complicated to present it here.

##### MSC:
 20M10 General structure theory for semigroups 20M05 Free semigroups, generators and relations, word problems
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