منابع مشابه
On controllers of prime ideals in group algebras of torsion-free abelian groups of finite rank
Let RA be a group ring of an abelian group A and let I be an ideal of RA . We say that a subgroup B of A controls I if I = (I ∩ RB)RA. The intersection c(I) of all subgroups of A controlling I is said to be the controller of the ideal I ; c(I) is the minimal subgroup of A which controls the ideal I . The ideal I is said to be faithful if I = A ∩ (1 + I) = 1. In theorem 4 we consider some method...
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The isomorphism problem for group algebras over a field with arbitrary characteristic of some special classes of torsion-free non-abelian groups is explored. Specifically, the following are proved: Suppose F is a field and G is a torsion-free group with centre C(G) such that FG ∼= FH as F -algebras for any group H . Then it is shown that H is torsion-free (provided that FG is without zero divis...
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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).
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It is known that many of the classes of simple Lie algebras of prime characteristic of nonclassical type have simple infinite-dimensional analogues of characteristic zero (see, for example, [4, p. 518]). We consider here analogues of those algebras which are defined by a modification of the definition of a group algebra. Thus we consider analogues of the Zassenhaus algebras as generalized by Al...
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Let G be a torsion-free abelian group of type (0, 0, 0, . . . ) and R an integrally closed integral domain with quotient field K. We show that every divisorial ideal (respectively, t-ideal) J of the group ring R[X;G] is of the form J = hIR[X;G] for some h ∈ K[X;G] and a divisorial ideal (respectively, t-ideal) I of R. Consequently, there are natural monoid isomorphisms Cl(R) ∼= Cl(R[X;G]) and C...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1969
ISSN: 0021-8693
DOI: 10.1016/0021-8693(69)90011-8