논문KCI 등재
DECOMPOSING NORMED UNITS IN COMMUTATIVE MODULAR GROUP RINGS
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We find a necessary and sufficient condition only in terms of the abelian p-group G and the perfect field F of characteristic p for the group V (FG) of normalized units in a group ring FG to be decomposed as G(1 + I2(FG;G)), where I(FG;G) is the augmentation ideal in FG. This sheds some light on the long-standing Direct Factor Problem.
Abstract
We find a necessary and sufficient condition only in terms of the abelian p-group G and the perfect field F of characteristic p for the group V (FG) of normalized units in a group ring FG to be decomposed as G(1 + I2(FG;G)), where I(FG;G) is the augmentation ideal in FG. This sheds some light on the long-standing Direct Factor Problem.
참고문헌 (7)
- P.V. Danchev, "Idempotent-nilpotent units in commutative group rings", Bull. Greek Math. Soc, 56, pp.21~28 (2009)
- P.V. Danchev, "Idempotent-nilpotent units of commutative group rings", Mathematica (Cluj), 54, pp.16~25 (2012)
- P.V. Danchev, "On decompositions of normed units in abelian group rings", J. Indones. Math. Soc, 18, pp.21~29 (2012)
- P.V. Danchev, "On a decomposition of normed unit groups in commutative group rings", Adv. Appl. Math. Sci, 11, pp.271~278 (2012)
- W.L. May, "Group algebras over nitely generated rings", J. Algebra, 38, pp.483~511 (1976)
- L. Fuchs, "Abelian Groups" (2015), Springer
- G. Karpilovsky, "Unit Groups of Group Rings" (1989), Longman Scientific and Technical
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