The isomorphic description of torsion units in commutative group rings over fields with positive characteristic.

Danchev, Peter

Displaying similar documents to “The isomorphic description of torsion units in commutative group rings over fields with positive characteristic.”

Commutative group algebras of highly torsion-complete abelian $p$ -groups

Peter Vassilev Danchev (2003)

Commentationes Mathematicae Universitatis Carolinae

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A new class of abelian $p$ -groups with all high subgroups isomorphic is defined. Commutative modular and semisimple group algebras over such groups are examined. The results obtained continue our recent statements published in Comment. Math. Univ. Carolinae (2002).

Warfield invariants in abelian group rings.

Peter V. Danchev (2005)

Extracta Mathematicae

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Let R be a perfect commutative unital ring without zero divisors of (R) = p and let G be a multiplicative abelian group. Then the Warfield p-invariants of the normed unit group V (RG) are computed only in terms of R and G. These cardinal-to-ordinal functions, combined with the Ulm-Kaplansky p-invariants, completely determine the structure of V (RG) whenever G is a Warfield p-mixed group.

Isomorphism of modular group algebras of direct sums of torsion-complete abelian $p$ -groups

Peter V. Danchev (1999)

Rendiconti del Seminario Matematico della Università di Padova

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Sylow P-Subgroups of Abelian Group Rings

Danchev, P. (2003)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 20C07, 20K10, 20K20, 20K21; Secondary 16U60, 16S34. Let PG be the abelian modular group ring of the abelian group G over the abelian ring P with 1 and prime char P = p. In the present article,the p-primary components Up(PG) and S(PG) of the groups of units U(PG) and V(PG) are classified for some major classes of abelian groups. Suppose K is a first kind field with respect to p in char K ≠ p and A is an abelian p-group. In the...

Isomorphism of Commutative Modular Group Algebras

Danchev, P. (1997)

Serdica Mathematical Journal

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∗ The work was supported by the National Fund “Scientific researches” and by the Ministry of Education and Science in Bulgaria under contract MM 70/91. Let K be a field of characteristic p > 0 and let G be a direct sum of cyclic groups, such that its torsion part is a p-group. If there exists a K-isomorphism KH ∼= KG for some group H, then it is shown that H ∼= G. Let G be a direct sum of cyclic groups, a divisible group or a simply presented torsion abelian group. Then...

A note on the isomorphism of modular group algebras of $p$ -mixed Abelian groups with divisible $p$ -components.

Danchev, Peter (2006)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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Torsion units in group rings.

Vikas Bist (1992)

Publicacions Matemàtiques

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Let U(RG) be the unit group of the group ring RG. In this paper we study group rings RG whose support elements of every torsion unit are torsion, where R is either the ring of integers Z or a field K.

Torsion matrices over commutative integral group rings.

Gregory T. Lee, Sudarshan K. Sehgal (2000)

Publicacions Matemàtiques

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Let ZA be the integral group ring of a finite abelian group A, and n a positive integer greater than 5. We provide conditions on n and A under which every torsion matrix U, with identity augmentation, in GL(ZA) is conjugate in GL(QA) to a diagonal matrix with group elements on the diagonal. When A is infinite, we show that under similar conditions, U has a group trace and is stably conjugate to such a diagonal matrix.