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Completely $0$-simple semirings

1971
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Transactions of the American Mathematical Society
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A completely (0-) simple semiring is a semiring R which is (0-) simple and is the union of its (0-) minimal left ideals and the union of its (0-) minimal right ideals. Structure results are obtained for such semirings. First the multiplicative semigroup of R is completely (0-) simple; for any Jf-class 7/(^0), H (u {0}) is a subsemiring. If furthermore R has a zero but is not a division ring, and if (H <J {0}, +) has a completely simple kernel for some H as above (for instance, if R is compact

doi:10.1090/s0002-9947-1971-0274531-8
fatcat:zukjnknxejfvteoypj2vdebcgi