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Ascending chain conditions on principal left and right ideals for semidirect products of semigroupsStopar, NikV članku raziščemo pogoje naraščajočih verig glavnih levih in desnih idealov za poldirektne produkte polgrup in pokažemo, kako je to povezano s pripadajočim problemom za kolobarje poševnih ... posplošenih potenčnih vrst. Naj bo ▫$S$▫ levo krajšljiva polgrupa z enoličnim idempotentom ▫$e, T$▫ desno krajšljiva polgrupa z idempotentom ▫$f$▫ in ▫$\omega: T \to \operatorname{End}(S)$▫ homomorfizem polgrup, za katerega velja ▫$\omega(f) = id_S$▫. Dokažemo, da v tem primeru poldirektni produkt ▫$S \rtimes_\omega T$▫ zadošča pogoju naraščajočih verig glavnih levih idealov (oz. desnih idealov) natanko tedaj, ko ▫$S$▫ in ▫$T$▫ zadoščata pogoju naraščajočih verig glavnih levih idealov (oz. desnih idealov in je ▫$\operatorname{Im} \omega(t)$▫ zaprta za popolne inverze za vse ▫$t \in T$▫). Podamo tudi več primerov, ki pokažejo, da za bolj splošne polgrupe te implikacije ne veljajo nujno.Source: Semigroup forum. - ISSN 0037-1912 (Vol. 85, no. 2, 2012, str. 322-336)Type of material - article, component partPublish date - 2012Language - englishCOBISS.SI-ID - 16373337
Author
Stopar, Nik
Topics
matematika |
algebra |
pogoj naraščajočih verig |
glavni ideal |
poldirektni produkt |
polgrupa |
krajšljivost |
mathematics |
algebra |
ascending chain condition |
principal ideal |
semidirect product |
semigroup |
cancellation property
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Stopar, Nik | 32023 |
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