Geodesic
Inner extensions of partial operations on a partial semigroup
Matematičeskie zametki SVFU, Tome 24 (2017) no. 2, pp. 30-45 Cet article a éte moissonné depuis la source Math-Net.Ru

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We analyse inner extensions of partial operations on a partial semigroup. The problem of extension of a partial operation internally to a full one with preservation of associativity is studied. The possibilities of continuing a partial operation on a partial semigroup of non-zero elements of a completely 0-simple semigroup by standard and non-standard methods are considered. A negative answer is obtained in relation to the question about whether any extension of a partial operation on a partial semigroup of non-zero elements is a completely simple semigroup, and whether any extension is standard. However, in certain cases the answers are positive. The article deduces the necessary and sufficient conditions of extendibility of a partial operation on a semigroup of residue modulo $n$, and also of a partial operation on a semigroup of non-zero elements of $(2\times 2)$-matrices over the field. The uniqueness of the extension of a partial operation on the semigroup of non-zero $(2\times 2)$-matrices over a field is shown.
Keywords: inner extension, partial semigroup, completely 0-simple semigroup, semi group of residue modulo n. 
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     author = {A. O. Petrikov},
     title = {Inner extensions of partial operations on a partial semigroup},
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     pages = {30--45},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2017_24_2_a2/}
}
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A. O. Petrikov. Inner extensions of partial operations on a partial semigroup. Matematičeskie zametki SVFU, Tome 24 (2017) no. 2, pp. 30-45. http://geodesic.mathdoc.fr/item/SVFU_2017_24_2_a2/

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