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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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