Results 31 to 40 of about 225,341 (216)
When are the natural embeddings of classical invariant rings pure?
Forum of Mathematics, Sigma, 2023 Consider a reductive linear algebraic group G acting linearly on a polynomial ring S over an infinite field; key examples are the general linear group, the symplectic group, the orthogonal group, and the special linear group, with the classical ...
Melvin Hochster +3 more
doaj +1 more source
Generalized twisted group rings [PDF]
Journal of Algebra, 2005 Let \(R\) be a Dedekind domain, and let \(G\) be an arbitrary group. The authors consider generalized group rings \(R*G\), twisted by a generalized 2-cocycle \(\alpha\colon G\times G\to R\setminus\{0\}\), i.e. with values not necessarily in \(R^\times\). Then \(H:=\{ x\in G\mid\alpha(x,x^{-1})\in R^\times\}\) is a subgroup of \(G\).
Nauwelaerts, E., Van Oystaeyen, Freddy
openaire +1 more source
Rings Graded By a Generalized Group
Topological Algebra and its Applications, 2014 The aim of this paper is to consider the ringswhich can be graded by completely simple semigroups.We show that each G-graded ring has an orthonormal basis, where G is a completely simple semigroup. Weprove that if I is a complete homogeneous ideal of a G-
Fatehi Farzad, Molaei Mohammad Reza
doaj +1 more source
Grothendieck Groups of Invariant Rings and of Group Rings
Journal of Algebra, 1994 Let \(G\) be a finite group acting as automorphisms of a (right) Noetherian ring \(S\), and \(R = S^ G\) be the fixed ring under this action. There is a Morita context linking the skew group ring \(T = S * G\) with \(R\), via the bimodules \(tT\) and \(Tt\) where \(t = \sum_{g \in G} g\). Suppose that the trace map \(\text{tr} : S \to R\) is surjective.
Brown, K.A., Lorenz, M.
openaire +2 more sources
Paraunitary matrices and group rings [PDF]
International Journal of Group Theory, 2014 Design methods for paraunitary matrices from complete orthogonal sets of idempotents and related matrix structuresare presented. These include techniques for designing non-separable multidimensional paraunitary matrices.
Barry Hurley, Ted Hurley
doaj
Skew group rings which are Galois
International Journal of Mathematics and Mathematical Sciences, 2000 Let S*G be a skew group ring of a finite group G over a ring S. It is shown that if S*G is an G′-Galois extension of (S*G)G′, where G′ is the inner automorphism group of S*G induced by the elements in G, then S is a G-Galois extension of SG.
George Szeto, Lianyong Xue
doaj +1 more source
Group Action on the Set of Nonunits in Rings
Journal of Mathematics, 2023 Let R be a ring, G be the group of all units of R, and X=R−G∪0. In this paper, we investigate avxx∈X=oxx∈X for a ring R, where avx is the set of all vertices of the zero-divisor graph of R adjacent to x.
Eman S. Almotairi +2 more
doaj +1 more source
Maximal quotient rings of group rings [PDF]
Pacific Journal of Mathematics, 1974 The two which have received the greatest attention are theclassical (Ore) quotient ring and the maximal (Utumi) quotient ring.The classical quotient ring has a relatively straightforward description,but it is only defined for rings which satisfy the so-called Ore con-dition.
openaire +3 more sources
On the structure of artinian-by-(finite rank) modules over generalized soluble groups
Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Matematika, 2014 Let R be a ring and G a group. An R-module A is said to be artinian-by-(finite rank), if $\mathrm{Tor}_R(A)$ is artinian and $A/\mathrm{Tor}_R(A)$ has finite R-rank.
V.A. Chupordia
doaj
Units in Abelian Group Algebras Over Direct Products of Indecomposable Rings
Cubo, 2012 Let R be a commutative unitary ring of prime characteristic p which is a direct product of indecomposable subrings and let G be a multiplicative Abelian group such that G0/Gp is nite.
Peter Danchev
doaj