Primitive group rings

Quasi-Primitive Rings and Density Theory

Primitive central idempotents of finite group rings of symmetric groups

Let p be a prime. We denote by Sn the symmetric group of degree n, by An the alternating group of degree n and by Fp the field with p elements. An important concept of modular representation theory of a finite group G is the notion of a block. The blocks are in one-to-one correspondence with block idempotents, which are the primitive central idempotents of the group ring FqG, where q is a prime...

0-primitive Near-rings, Minimal Ideals and Simple Near-rings

We study the structure of 0-primitive near-rings and are able to answer an open question in the theory of minimal ideals in near-rings to the negative, namely if the heart of a zero symmetric subdirectly irreducible near-ring is subdirectly irreducible again. Also, we will be able to classify when a simple near-ring with an identity and containing a minimal left ideal is a Jacobson radical near...

On primitive ideals in polynomial rings over nil rings

Let R be a nil ring. We prove that primitive ideals in the polynomial ring R[x] in one indeterminate over R are of the form I [x] for some ideals I of R. All considered rings are associative but not necessarily have identities. Köthe’s conjecture states that a ring without nil ideals has no one-sided nil ideals. It is equivalent [4] to the assertion that polynomial rings over nil rings are Jaco...

COTORSION DIMENSIONS OVER GROUP RINGS

Let $Gamma$ be a group, $Gamma'$ a subgroup of $Gamma$ with finite index and $M$ be a $Gamma$-module. We show that $M$ is cotorsion if and only if it is cotorsion as a $Gamma'$-module. Using this result, we prove that the global cotorsion dimensions of rings $ZGamma$ and $ZGamma'$ are equal.