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The Jordan-Hölder theorem for semirings.

Francisco Poyatos (1980)

Revista Matemática Hispanoamericana

The object of this paper is to prove the Green and Jordan-Hölder theorems in semirings. We follow Rees [11], Green [5], Clifford and Preston [2]. This work is similar to [7] and generalizes [8] and [9]. Although some proofs are parallel to those for semigroups, we explain them here to obtain a complete and self-contained exposition.

The semiring of 1-preserving endomorphisms of a semilattice

Jaroslav Ježek, Tomáš Kepka (2009)

Czechoslovak Mathematical Journal

We prove that the semirings of 1-preserving and of 0,1-preserving endomorphisms of a semilattice are always subdirectly irreducible and we investigate under which conditions they are simple. Subsemirings are also investigated in a similar way.

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