This article is cited in 1 paper

Mathematical logic, algebra and number theory

Functional representations of lattice-ordered semirings. II

O. V. Chermnykh

Vyatka state universite, Moskovskaya, 36, 610000, Kirov, Russia

Abstract: The article considers the lattice-ordered semirings ($drl$-semirings). Two sheaves of $drl$-semirings are constructed. The first sheaf is based on prime spectrum of $l$-ideals. The idea of construction is close to the well-known sheaf of germs of continuous functions. The second sheaf resembles Pierce's sheaf of abstract rings or semirings. Its basis space is Boolean space of maximal ideals of the lattice of complemented $l$-ideals from $drl$-semiring. The main results are theorems on representations of an $l$-semiprime and an arbitrary $drl$-semirings by sections of corresponding sheaves.

Keywords: lattice-ordered semiring, sheaf, sheaf representation.

UDC: 512.25

MSC: 16Y60

Received April 1, 2018, published June 1, 2018

DOI: 10.17377/semi.2018.15.053

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