Ternary rings of Pappian planes
Ternary rings with zero associated to Desarguesian and Pappian planes
Ternary rings with zero associated to translation planes
The inverse semigroup of a sumordered semiring.
The Jordan-Hölder theorem for semirings.
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 Maslov dequantization, idempotent and tropical mathematics: a brief introduction.
The semiring of 1-preserving endomorphisms of a semilattice
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.
The tropical Grassmannian.
Theory of hyperrings and hyperfields.