FMF, Mathematical Library, Lj. (MAKLJ)
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Delno urejene polgrupe in delno urejeni polkolobarji : magistrsko deloRojko, CvetkaPrvo poglavje vsebuje pregled osnovnih pojmov iz teorije algebrskih struktur in teorije urejenostnih struktur. Drugo poglavje začnemo s teorijo splošnih delno urejenih grupoidov in polgrup, ki jo ... zelo hitro poglobimo z dodatnimi zahtevami. Obdelamo lastnosti stožcev delno urejenih polgrup in najdemo povezavo med delno urejeno grupo in delno urejeno polgrupo kot njenim pozitivnim stožcem. Vpeljemo pojme pozitivno urejena, naravno urejena in arhimedska delno urejena polgrupa ter linearno urejena polgrupa. Dokažemo, da je arhimedska naravno linearno urejena polgrupa pri določenih pogojih urejenostno izomorfna aditivni polgrupi naravnih števil. Poglavje zaključimo sposegom v teorijo mrežno urejenih polgrup. V tretjem poglavju se posvetimo najprej teoriji polkolobarjev, v kateri obdelamo pojme aditivna in multiplikativna idempotentnost, aditivna in multiplikativna obrnljivost, enostavni polkolobarji ter uvedemo pojem polobsega. Nadalje dopolnimo polkolobar z delno urejenostjo in pregledamo teorijo delno urejenih polkolobarjev ter homomorfizmov polkolobarjev. Pokažemo, da obstaja enolično določen homomorfizem polkolobarjev iz polkolobarja pozitivnih racionalnih števil v polobseg brez ničelne vsote. Poglavje sklenemo s pogledom v teorijo mrežno urejenih polkolobarjev, ki je zaradi močnejših zahtev nekoliko bogatejša od teorije mrežno urejenih polgrup.Type of material - master's thesis ; adult, seriousPublication and manufacture - Ljubljana : [C. Rojko], 1998Language - slovenianCOBISS.SI-ID - 8488537
Author
Rojko, Cvetka
Other authors
Lavrič, Boris
Topics
polgrupe |
delna urejenost |
polkolobarji |
polobsegi |
mrežna urejenost |
semigroups |
partial order |
hemirings |
semirings |
semifields |
lattice order
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Skladišče-Jadranska 21 0000011052/0000000018 Skladišče-Jadranska 21 11052/18 |
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Rojko, Cvetka | 23275 |
Lavrič, Boris | 05000 |
Source: Personal bibliographies
and: SICRIS
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