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Isomorphism of modular group algebras of abelian groups with semi-complete $p$-primary components

Peter Danchev
대한수학회 (The Korean Mathematical Society)|2007.04|대한수학회논문집 (Communications of the KMS)|제22권 제2호|pp. 157-161

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Abstract

Let G be a p-mixed abelian group with semi-complete torsionsubgroup G_t such that G is splitting or is of torsion-freerank one, and let R be a commutative unitary ring of primecharacteristic p. It is proved that the group algebras RG andRH are R-isomorphic for any group H if and only if G andH are isomorphic. This isomorphism relationship extends ourearlier results in (Southeast Asian Bull. Math., 2002), (Proc.Amer. Math. Soc., 2002) and (Bull. Korean Math. Soc., 2005) aswell as completely settles a problem posed by W. May in (Proc.Amer. Math. Soc., 1979).

참고문헌 (13)

  1. "Commutative group algebras of sigma-summable abelian groups", 125(9), pp.2559~2564 (1997)
  2. "Isomorphism of modular group algebras of direct sums oftorsion-complete abelian p-groups", 101, pp.51~58 (1999)
  3. "Isomorphism of modular group algebras of totally projectiveabelian groups", 28(5), pp.2521~2531 (2000)
  4. "Commutative group algebras of cardinalityaleph_1", 25(4), pp.589~598 (2002)
  5. "Isomorphism of commutative group algebras of closedp-groups and p-local algebraically compact groups", 130(7), pp.1937~1941 (2002)
  6. "Commutative group algebras of direct sums ofsigma-summable abelian p-groups", 45(2), pp.1~15 (2003)
  7. "Commutative group algebras ofp^{omega+n-projective abelian groups}", 29(3), pp.259~270 (2004)
  8. "Isomorphic modular group algebras of semi-complete primaryabelian groups", 42(1), pp.53~56 (2005)
  9. "Commutative modular groupalgebras of special classes of abelian groups"
  10. Irwin, "Countable direct sums of torsion completegroups", pp.763~ (1966)
  11. "Modular group algebras of totally projectivep-primary groups", (1), pp.31~ (1979)
  12. no. 2, "Modular group algebras of simply presented abelian groups", pp.403~ (1988)
  13. "On mixed groups of torsion-free rank one", pp.134~ (1967)

관련 논문AI추천

Isomorphic modular group Algebras of semi-complete primary Abelian groupsPeter V. Danchev대한수학회 · 대한수학회보2005 · 제42권 제1호Simple Presentness in Modular Group Algebras over Highly-generated RingsPeter V. Danchev경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2006 · 제46권 제1호DECOMPOSING NORMED UNITS IN COMMUTATIVE MODULAR GROUP RINGSPeter V. Danchev장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제1호Augmentation quotients of integral group rings이준걸대한수학회 · 대한수학회보2008 · 제45권 제1호The structure of the radical of the non semisimple group rings유원석강원경기수학회 · 한국수학논문집2010 · 제18권 제1호Commutative Group Algebras of Direct Sums of Countable Abelian GroupsPeter Danchev경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2004 · 제44권 제1호

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