1 - 10 of 13 articles
Let G be a group with a dihedral subgroup H of order 2p
, where p is an odd prime. We show that if there exist H-connected transversals in G, then G is a solvable group. We apply this result to the loop theory and show that if the inner mapping group of a finite loop Q is dihedral of order 2p...
For H a finite-dimensional Hopf algebra over a field k, we study H*-Galois Azumaya extensions A, i.e., A is an H-module algebra which is H*-Galois with A/A
separable and A
Azumaya. We prove that there is a Galois correspondence between a set of separable subalgebras of A and a set of...
We study the lattice. C(S) of congruences of a monoid S which is the Bruck-Reilly extension of a monoid T by a homomorphism α. The inclusion, meet and join of congruences are described in terms of congruences and ideals of T. We show that C(S) can be naturally decomposed into three sublattices,...
A lattice-theoretic approach to the radical theory of rings was initiated by Snider. In the current paper, we extend this approach to the radical theory of involution rings. We show that the classes of hereditary radicals, radicals satisfying ADS and invariant radicals form complete sublattices...
Let G be a group, ZG the integral group ring of G, and I(G) its augmentation ideal. Let H be a subgroup of G. It is proved that the subgroup of G determined by the product I(H)I(G)I(H) equals γ3(H), i.e., the third term in the lower central series of H. Also, the subgroup determined by I(H)I(G)I...
A finite semigroup S is said to preserve finite generation (resp., presentability) in direct products, provided that, for every infinite semigroup T, the direct product S × T is finitely generated (resp., finitely presented) if and only if T is finitely generated (resp., finitely presented). The...
The structure of groups in which many subgroups have a certain property X has been investigated for several choices of the property X. Groups whose non-normal subgroups satisfy certain finite rank conditions are studied in this article. In particular, a classification of groups in which every...
Let R be a prime ring with no non-zero nil one-sided ideals, d a nonzero derivation on R, and f(X
) a multilinear polynomial not central-valued on R. Suppose d(f(x
)) is either invertible or nilpotent for all x
in some non-zero ideal of R. Then it is proved that...
In this paper, we introduce the concept of graded Morita–Takeuchi contexts and prove that every graded Morita–Takeuchi context induces a Morita–Takeuchi context between the 1-components of the corresponding coalgebras. We also establish an action of Morita–Takeuchi contexts on graded coalgebras,...
For a finite group G and a subgroup A of Aut(G), let M
(G) denote the centralizer near-ring determined by A and G. The group G is an M
(G)-module. Using the action of M
(G) on G, one has the n × n generalized matrix near-ring Mat
(G);G). The correspondence between the ideals of...
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