Simple quotient rings of group algebras

Generalized Quotient Rings

Maximal Quotient Rings and Essential Right Ideals in Group Rings of Locally Finite Groups

MAXIMAL QUOTIENT RINGS AND ESSENTIAL RIGHT IDEALS IN GROUP RINGS OF LOCALLY FINITE GROUPS Theorem . zero . FERRAN CEDÓ * AND BRIAN HARTLEY Dedicated to the memory of Pere Menal Let k be a commutative field . Let G be a locally finite group without elements of order p in case char k = p > 0 . In this paper it is proved that the type I. part of the maximal right quotient ring of the group algebgr...

Gelfand-Kirillov Dimension of Commutative Subalgebras of Simple Infinite Dimensional Algebras and their Quotient Division Algebras

Throughout this paper, K is a field, a module M over an algebra A means a left module denoted AM , ⊗ = ⊗K . In contrast to the finite dimensional case, there is no general theory of central simple infinite dimensional algebras. In some sense, structure of simple finite dimensional algebras is ‘determined’ by their maximal commutative subalgebras (subfields)[see [18] for example]. Whether this s...

Complete Quotient Boolean Algebras

For I a proper, countably complete ideal on P(X) for some set X , can the quotient Boolean algebra P(X)/I be complete? This question was raised by Sikorski [Si] in 1949. By a simple projection argument as for measurable cardinals, it can be assumed that X is an uncountable cardinal κ, and that I is a κ-complete ideal on P(κ) containing all singletons. In this paper we provide consequences from ...

Hyperbolicity of orders of quaternion algebras and group rings

For a given division algebra of the quaternions, we construct two types of units of its Z-orders: Pell units and Gauss units. Also, if K = Q √ −d, d ∈ Z \ {0, 1} is square free and R = IK , we classify R and G such that U1(RG) is hyperbolic. In particular, we prove that U1(RK8) is hyperbolic iff d > 0 and d ≡ 7 (mod 8). In this case, the hyperbolic boundary ∂(U1(RG)) ∼= S, the two dimensional s...