The direct factor problem for modular abelian group algebras

1989 ◽  
pp. 303-308 ◽  
Author(s):  
Warren May
Keyword(s):  
Abelian Group ◽  
Group Algebras ◽  
Direct Factor ◽  
Factor Problem

JOINT COMPLEMENTS AND ISOMORPHISM OF MODULAR ABELIAN GROUP ALGEBRAS

2013 ◽  
Vol 12 (07) ◽  
pp. 1350035 ◽  
Author(s):  
WARREN MAY
Keyword(s):  
Abelian Group ◽  
Isomorphism Problem ◽  
Group Algebras ◽  
Prime Characteristic ◽  
Direct Factor ◽  
Perfect Field ◽  
Factor Problem

For modular abelian group algebras over a perfect field of prime characteristic, a connection is given between the direct factor problem and the isomorphism problem.

Commutative Modular Group Algebras of Special Classes of Abelian Groups

2013 ◽  
Vol 59 (2) ◽  
pp. 415-430
Author(s):  
P.V. Danchev
Keyword(s):  
Modular Group ◽  
Abelian Groups ◽  
Classification Problem ◽  
Isomorphism Problem ◽  
Group Algebras ◽  
Direct Factor ◽  
Factor Problem ◽  
Special Classes

Abstract Structural results on the Direct Factor Problem, the Classification Problem and the Isomorphism Problem are proved for modular group algebras of certain sorts of abelian groups.

WARFIELD INVARIANTS IN COMMUTATIVE GROUP ALGEBRAS

2008 ◽  
Vol 07 (03) ◽  
pp. 337-346 ◽  
Author(s):  
PETER V. DANCHEV
Keyword(s):  
Abelian Group ◽  
Prime Number ◽  
Group Algebra ◽  
Ordinal Number ◽  
Commutative Group ◽  
Group Algebras

Let F be a field and G an Abelian group. For every prime number q and every ordinal number α we compute only in terms of F and G the Warfield q-invariants Wα, q(VF[G]) of the group VF[G] of all normed units in the group algebra F[G] under some minimal restrictions on F and G. This expands own recent results from (Extracta Mathematicae, 2005) and (Collectanea Mathematicae, 2008).

scholarly journals Invariant ideals of abelian group algebras under the multiplicative action of a field. II

2001 ◽  
Vol 130 (4) ◽  
pp. 951-957 ◽  
Author(s):  
J. M. Osterburg ◽  
D. S. Passman ◽  
A. E. Zalesskiĭ
Keyword(s):  
Abelian Group ◽  
Group Algebras

Minimal ideals in finite abelian group algebras and coding theory

2016 ◽  
Vol 10 (2) ◽  
pp. 321-340
Author(s):  
Gladys Chalom ◽  
Raul Antonio Ferraz ◽  
Marinês Guerreiro
Keyword(s):  
Abelian Group ◽  
Coding Theory ◽  
Finite Abelian Group ◽  
Group Algebras

Derivations on group algebras of a locally compact abelian group

2015 ◽  
Vol 180 (3) ◽  
pp. 595-605 ◽  
Author(s):  
Mohammad Javad Mehdipour ◽  
Zahra Saeedi
Keyword(s):  
Abelian Group ◽  
Compact Abelian Group ◽  
Group Algebras ◽  
Locally Compact Abelian Group ◽  
Locally Compact

scholarly journals Abelian group algebras of finite order

1950 ◽  
Vol 68 (3) ◽  
pp. 420-420 ◽  
Author(s):  
Sam Perlis ◽  
Gordon L. Walker
Keyword(s):  
Abelian Group ◽  
Finite Order ◽  
Group Algebras

VECTOR INVARIANT IDEALS OF ABELIAN GROUP ALGEBRAS UNDER THE ACTION OF THE SYMPLECTIC GROUPS

2013 ◽  
Vol 12 (08) ◽  
pp. 1350046
Author(s):  
JIZHU NAN ◽  
LINGLI ZENG
Keyword(s):  
Abelian Group ◽  
Finite Field ◽  
Vector Space ◽  
Group Algebra ◽  
Symplectic Group ◽  
Group Algebras ◽  
Symplectic Groups ◽  
Vector Invariant

Let F be a finite field and let Sp 2ν(F) be the symplectic group over F. If Sp 2ν(F) acts on the F-vector space F2ν, then it can induce an action on the vector space F2ν ⊕ F2ν, defined by (x, y)A = (xA, yA), ∀ x, y ∈ F2ν, A ∈ Sp 2ν(F). If K is a field with char K ≠ char F, then Sp 2ν(F) also acts on the group algebra K[F2ν ⊕ F2ν]. In this paper, we determine the structures of Sp 2ν(F)-stable ideals of the group algebra K[F2ν ⊕ F2ν] by augmentation ideals, and describe the relations between the invariant ideals of K[F2ν] and the vector invariant ideals of K[F2ν ⊕ F2ν].

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