On Pierce stalks of semirings. (English. Russian original) Zbl 1342.16044

Markov, R. V.; Chermnykh, V. V.

J. Math. Sci., New York 213, No. 2, 243-253 (2016); translation from Fundam. Prikl. Mat. 19, No. 2, 171-186 (2014).

From the introduction: In this paper, we investigate Pierce stalks of semirings and we study properties of semirings lifted from properties of Pierce stalks. We distinguish classes of semirings that allow us to get characterizations by properties of their Pierce sheaves. We use algebraic properties of Pierce stalks for describing the semirings under study. Because of difficulties that arise, sometimes we have to use some properties of sheaves or spectra of semirings.

MSC:

16Y60	Semirings
16S60	Associative rings of functions, subdirect products, sheaves of rings

Keywords:

spectra of semirings; sheaves of semirings; Pierce stalks; Pierce sheaves

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