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13.
The ▫$n$▫-insertive subgroups of units
Dolžan, David
Naj bo ▫$R$▫ končni kolobar, ▫$G$▫ njegova grupa enot, ▫$J$▫ pa Jacobsonov radikal. Naj bo še ▫$n$▫ poljubno celo število. Dokažemo, da je ▫$R$▫ ▫$n$▫-vstavljivi kolobar natanko tedaj, ko je ▫$G$▫ ...▫$n$▫-vstavljiva grupa in pokažemo, da je vsak ▫$n$▫-vstavljivi končni kolobar direktna vsota lokalnih kolobarjev. Dokažemo tudi, da je v primeru, ko je ▫$n$▫ enota, lokalni kolobar ▫$R$▫ ▫$n$▫-vstavljiv natanko tedaj, ko je njegova Jacobsonova grupa ▫$1+J$▫ ▫$n$▫-vstavljiva in najdemo primer, da to ne drži, če ▫$n$▫ ni enota.
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