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Simple Presentness in Modular Group Algebras over Highly-generated Rings

Peter V. Danchev
경북대학교 자연과학대학 수학과|2006.03|Kyungpook Mathematical Journal|제46권 제1호|pp. 57-64

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Abstract

It is proved that ifG is a direct sum of countable abelianp-groups and Ris a special selected commutative unitary highly-generated ring of prime characteristicp,which ring is more general than the weakly perfect one, then the group of all normed unitsV(RG) modulo G, that isV(RG)=G, is a direct sum of countable groups as well. Thisstrengthens a result due to W. May, published in (Proc. Amer. Math. Soc., 1979), thattreats the same question but over a perfect ring.

참고문헌 (7)

  1. "Modular group algebras of coproducts of countable abelian groups", 29(2) (2000)
  2. "Commutative group algebras of direct sums of countable abelian groups", 44(1) (2004)
  3. "Commutative group algebras of direct sums of-summable abelian p-groups", 45(2), pp.1~15 (2003)
  4. "withoutR being weakly perfect orcountable", vietnam j. math.
  5. "Proc. Amer. Math. Soc.", 76 1, pp.31~ (1979)
  6. "Proc. Amer. Math. Soc.", 104 2, pp.403~ (1988)
  7. "The direct factor problem for modular abelian group algebras", 93, pp.303~ (1989)

관련 논문AI추천

Isomorphism of modular group algebras of abelian groups with semi-complete $p$-primary componentsPeter Danchev대한수학회 · 대한수학회논문집2007 · 제22권 제2호Isomorphic modular group Algebras of semi-complete primary Abelian groupsPeter V. Danchev대한수학회 · 대한수학회보2005 · 제42권 제1호Semi-Primeness of the Endomorphism Ring of a Projective ModuleSoon-Sook Bae대한수학회 · 대한수학회논문집2003 · 제18권 제4호Injective Envelopes of Simple Modules over Polynomial RingsZhongming Tang대한수학회 · 대한수학회보2005 · 제42권 제1호Augmentation quotients of integral group rings이준걸대한수학회 · 대한수학회보2008 · 제45권 제1호On weak $\Pi$-regularity and the simplicity of prime factor rings김진용, Hai Lan Jin대한수학회 · 대한수학회보2007 · 제44권 제1호

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