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Loop near-rings and unique decompositions of H-spaces
Franetič, Damir ; Pavešić, Petar
Za vsak H-prostor ▫$X$▫ ima množica homotopskih razredov preslikav ▫$X$▫ vase naravno algebraično strukturo skoraj-kolobarja. Čeprav je v splošnem stuktura skoraj-kolobarjev zelo zapletena, tisti, ki ...so porojeni z endomorfizmi H-prostorov so dovolj sorodni običajnim kolobarjem, da dopuščajo teorijo razcepov Krull-Schmidtovega tipa, le-to pa lahko uporabimo pri izrekih o razcepih H-prostorov. Kot posledico razcepov modulov nad skoraj-kolobarji izpeljemo izreke o enoličnih razcepih H-prostorov. Dodatno lahko dobimo rezultate o razcepih za nekatere neskončne produkte H-prostor zahvaljujoč nekaterim recentnim rezultatom teorije neskončnih produktov. Na koncu pokažemo, da so nerazcepni ▫$p$▫-lokalni H-prostori avtomatično tudi krepko nerazcepni, kar nas pripelje do preprostega alternativnega dokaza klasičnih izrekov o enolični faktorizaciji C. Wilkersona in B. Graya.
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