Completely 0-simple semirings
Mireille Poinsignon Grillet and Pierre-Antoine Grillet
Trans. Amer. Math. Soc. 155 (1971), 19-33
Primary 16.96; Secondary 20.00
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Abstract: A completely simple semiring is a semiring which is simple and is the union of its minimal left ideals and the union of its minimal right ideals. Structure results are obtained for such semirings. First the multiplicative semigroup of is completely simple; for any -class is a subsemiring. If furthermore has a zero but is not a division ring, and if has a completely simple kernel for some as above (for instance, if is compact or if the -classes are finite), then (i) is idempotent; (ii) has no zero divisors, additively or multiplicatively. Additional results are given, concerning the additive -classes of and also minimal ideals of semirings in general.
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Completely 0-simple semirings,
completely simple semiring,
minimal left ideal,
minimal right ideal,
0-minimal left ideal,
0-minimal right ideal,
Green's relations of a semigroup,
Green's relations of a semiring,
compact simple semiring,
finite simple semiring,
left translations of a semiring
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American Mathematical Society