Extension of a Semigroup Embedding Theorem to Semirings
Canadian mathematical bulletin, Tome 18 (1975) no. 2, pp. 297-298
Voir la notice de l'article provenant de la source Cambridge University Press
It is well known [1,3] that a commutative semigroup (S, +) can be embedded in a semigroup which is a union of groups if and only if S is separative (2a = a + b = 2b implies a = b). We extend this result to additively commutative semirings.A semiring (S, +, ⋅) is a set S with associative addition (+) and multiplication (⋅), the latter distributing over addition from left and right. In what follows (S, +, ⋅) will denote a semiring in which the additive semigroup (S, +) is commutative. An element 0 can be adjoined, where s = s + 0, 0 = 0 ⋅ s = s ⋅ 0 for all s in S, to form S°.
Extension of a Semigroup Embedding Theorem to Semirings. Canadian mathematical bulletin, Tome 18 (1975) no. 2, pp. 297-298. doi: 10.4153/CMB-1975-057-1
@misc{10_4153_CMB_1975_057_1,
title = {Extension of a {Semigroup} {Embedding} {Theorem} to {Semirings}},
journal = {Canadian mathematical bulletin},
pages = {297--298},
year = {1975},
volume = {18},
number = {2},
doi = {10.4153/CMB-1975-057-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-057-1/}
}
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