Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 677–684
This article is cited in 1 scientific paper (total in 1 paper)
Mathematical logic, algebra and number theory
Functional representations of lattice-ordered semirings. II
O. V. Chermnykh
Vyatka state universite,
610000, Kirov, Russia
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.
lattice-ordered semiring, sheaf, sheaf representation.
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Received April 1, 2018, published June 1, 2018
O. V. Chermnykh, “Functional representations of lattice-ordered semirings. II”, Sib. Èlektron. Mat. Izv., 15 (2018), 677–684
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\paper Functional representations of lattice-ordered semirings. II
\jour Sib. \`Elektron. Mat. Izv.
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V. V. Chermnykh, O. V. Chermnykh, “Funktsionalnye predstavleniya reshetochno uporyadochennykh polukolets. III”, Tr. IMM UrO RAN, 26, no. 3, 2020, 235–248
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