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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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##### References:
 [1] Dombi E., Acta Sci. Math. (Szeged) 69 pp 569– (2003) [2] DOI: 10.1017/S0017089500009873 · Zbl 0802.20051 [3] DOI: 10.1142/S0218196709005214 · Zbl 1192.20041 [4] DOI: 10.1142/S0218196799000412 · Zbl 0948.20036 [5] DOI: 10.1080/00927870701509503 · Zbl 1144.20037 [6] Grätzer G., Universal Algebra (1979) [7] DOI: 10.1007/s00233-006-0618-1 · Zbl 1144.20042 [8] Lawson M. V., Glasgow Math. J. 36 pp 97– (1994) · Zbl 0820.20070 [9] DOI: 10.1142/9789812816689 [10] McAlister D. B., Trans. Amer. Math. Soc. 192 pp 227– (1974) [11] DOI: 10.1090/S0002-9947-74-99950-4 [12] McAlister D. B., J. Austral. Math. Soc. 22 pp 188– (1976) [13] McAlister D. B., Pacific J. Math. 68 pp 161– (1977) · Zbl 0368.20043 [14] DOI: 10.1142/S0218196793000214 · Zbl 0796.20053 [15] Szendrei M. B., Internat. J. Algebra Comput. 21 pp 1037– (2012) · Zbl 1246.20052 [16] Szendrei M. B., J. Algebra Comput. 22 (2012)
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