共查询到20条相似文献,搜索用时 15 毫秒
1.
A. E. Zalesski 《Israel Journal of Mathematics》1996,96(2):609-621
The paper discusses approaches to constructing two-sided ideals of the modular group algebra of finitary symmetric group.
In memory of Professor S. A. Amitsur 相似文献
2.
3.
Peter J. Wood 《Proceedings of the American Mathematical Society》2000,128(2):445-451
In this paper we provide a necessary condition for a closed ideal in the Fourier algebra of a locally compact amenable group to be completely complemented. The classification of completely complemented ideals is completed in the case of an amenable discrete group. We also investigate the ideals possessing a bounded approximate identity.
4.
We investigate and characterize ideals in a group algebra KG which have complementary duals, i.e., ideals C in KG which satisfy \(KG = C \oplus C^\perp .\) In the special case that G is a cyclic group we get an early result of Yang and Massey as an easy consequence. 相似文献
5.
Jacques Thévenaz 《代数通讯》2013,41(4):391-425
We characterize principal nilpotent ideals in finite abelian group algebra Fq [G] (Fq a finite field of ps elements, p prime), with greatest possible dimension. We prove also that the-se ideals are all isomorphic. 相似文献
6.
A. R. Kemer 《Mathematical Notes》2012,92(3-4):375-382
We prove that any nonzero ideal of the group algebra of the infinite symmetric group over a field of nonzero characteristic contains skew-symmetric and symmetric elements of sufficiently large order. Using this result, we reduce the question of the classification of the ideals of the group algebra of the infinite symmetric group to the classification of certain subspaces of the tensor square of a finitely generated free associative algebra. 相似文献
7.
In this paper we find upper bounds for the nilpotency degree of some ideals in the cohomology ring of a finite group by studying fixed point free actions of the group on suitable spaces. The ideals we study are the kernels of restriction maps to certain collections of proper subgroups. We recover the Quillen-Venkov lemma and the Quillen F-injectivity theorem as corollaries, and discuss some generalizations and further applications.We then consider the essential cohomology conjecture, and show that it is related to group actions on connected graphs. We discuss an obstruction for constructing a fixed point free action of a group on a connected graph with zero “k-invariant” and study the class related to this obstruction. It turns out that this class is a “universal essential class” for the group and controls many questions about the groups essential cohomology and transfers from proper subgroups. 相似文献
8.
Czeslaw Bagiński 《代数通讯》2019,47(2):761-771
The modular isomorphism problem is settled for 3-groups of maximal class but two families of groups. Moreover, the conjecture that the ideals belonging to the lower central series of a group base are determined by the structure of the group algebra is refuted in greatest generality by virtue of a single group of order 81 of maximal class, and it is proved that the nilpotency class is determined by the structure of the group algebra for p-groups of maximal class. 相似文献
9.
In this paper, we extend some results of D.Dolzan on finite rings to profinite rings, a complete classification of profinite
commutative rings with a monothetic group of units is given. We also prove the metrizability of commutative profinite rings
with monothetic group of units and without nonzero Boolean ideals. Using a property of Mersenne numbers, we construct a family
of power 2ℵ0 commutative non-isomorphic profinite semiprimitive rings with monothetic group of units. 相似文献
10.
Joseph Max Rosenblatt 《Journal of Functional Analysis》1976,21(1):31-51
For a nondiscrete σ-compact locally compact Hausdorff group G, L∞(G) is a commutative Banach algebra under pointwise multiplication which has many nonzero proper closed invariant ideals; there is at least a continuum of maximal invariant ideals {Nα} such that Nα1 + Nα2 = L∞(G) whenever α1 ≠ α2. It follows from the construction of these ideals that when G is also amenable as a discrete group, then LIM?TLIM contains at least a continuum of mutually singular elements each of which is singular to any element of TLIM. The supports of left-invariant means are in the maximal ideal space of L∞(G); the structure of these supports leads to the notion of stationary and transitive maximal ideals. To prove that both these types of maximal ideals are dense among all maximal ideals, one shows that the intersection of all nonzero closed invariant ideals is zero. This is the case even though the intersection of any sequence of closed invariant ideals is not zero and the intersection of all the maximal invariant ideals is not zero. 相似文献
11.
Martin Lorenz 《Transformation Groups》2009,14(3):649-675
Let G be an affine algebraic group and let R be an associative algebra with a rational action of G by algebra automorphisms. We study the induced G-action on the set Spec R of all prime ideals of R, viewed as a topological space with the Jacobson–Zariski topology, and on the subspace Rat R ⊆ Spec R consisting of all rational ideals of R. Here, a prime ideal P of R is said to be rational if the extended centroid is equal to the base field. Our results generalize the work of Mœglin and Rentschler and of Vonessen to arbitrary associative
algebras while also simplifying some of the earlier proofs.
The map P ↦ ⋂
g ∈ G
g.P gives a surjection from Spec R onto the set G-Spec R of all G-prime ideals of R. The fibers of this map yield the so-called G-stratification of Spec R which has played a central role in the recent investigation of algebraic quantum groups, in particular, in the work of Goodearl
and Letzter. We describe the G-strata of Spec R in terms of certain commutative spectra. Furthermore, we show that if a rational ideal P is locally closed in Spec R then the orbit G.P is locally closed in Rat R. This generalizes a standard result on G-varieties. Finally, we discuss the situation where G-Spec R is a finite set.
Research supported in part by NSA Grant H98230-07-1-0008. 相似文献
12.
Erhard Aichinger 《Journal of Pure and Applied Algebra》2006,205(1):74-93
Let V be a finite expanded group, e.g., a ring or a group. We investigate the near-ring 〈C0(V);+,°〉 of zero-preserving congruence-preserving functions on V. We obtain some information on the structure of 〈C0(V);+,°〉 from the lattice of ideals of V: for example, the number of maximal ideals of 〈C0(V);+,°〉 is completely determined by the isomorphism class of the ideal lattice of V. 相似文献
13.
Teruo Takeuchi 《manuscripta mathematica》1982,39(1):99-109
Let l be an odd prime, and k an algebraic number field of a finite degree. Let S be a finite product of distinct prime ideals g of k such that Ng1 (mod l). Let I(s) (resp. P(s)) denote the group of ideals (resp. principal ideals) of k prime to S, and let PS denote the ray modulo S. In this paper we prove that the order (resp. the l-rank) of I(S)/P(S)lPS is expressed by the decomposition groups of prime factors of S in a Galois extension Ko (resp. Kr) over k. As an application of this, some results about genus theory are obtained. 相似文献
14.
《Journal of Pure and Applied Algebra》2023,227(8):107344
We derive a family of prime ideals of the Burnside Tambara functor for a finite group G. In the case of cyclic groups, this family comprises the entire prime spectrum. We include some partial results towards the same result for a larger class of groups. 相似文献
15.
The automorphism group of the Toeplitz algebra on H2(T2) 总被引:1,自引:0,他引:1
The automorphism group of the C*-algebra generated by the Toeplitz operatos with symbols being continuous functions on the bicircle is characterized completely.The investigation is based on the analysis of the behaviour of an automorphism of theToeplitz algebra on its C*-ideal chains, and the state of the closed ideals in C(T)(×)(h)(H). 相似文献
16.
Rudolf Tange 《Mathematische Zeitschrift》2012,271(1-2):157-165
Let H be an algebraic group scheme over a field k acting on a commutative k-algebra A which is a unique factorisation domain. We show that, under certain mild assumptions, the monoid of nonzero H-stable principal ideals in A is free commutative. From this we deduce, in certain special cases, results about the monoid of nonzero semi-invariants and the algebra of invariants. We use an infinitesimal method which allows us to work over an arbitrary base field. 相似文献
17.
Prof. Dr. Eberhard Kaniuth 《Monatshefte für Mathematik》1982,93(4):293-302
LetG be a -compact locally compact group such thatG/Z(G), whereZ(G) denotes the center ofG, has a relatively compact commutator subgroup. It is shown that primary ideals inL
1(G) are maximal. 相似文献
18.
P. G. Zograf 《Journal of Mathematical Sciences》1982,19(6):1637-1652
In the paper the Selberg trace formula is derived for the Hilbert modular group of a real quadratic algebraic number field with one class of ideals, acting on the product of two upper semiplanes.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 100, pp. 26–47, 1980. 相似文献
19.
Emanuela De Negri 《代数通讯》2013,41(12):4415-4426
In this paper we study the rings defined by ideals of pfaffians of a skew symmetric matrix of indeterminates. We analyze the case in which the pfaffians are not necessarily of fixed size. We prove that such rings are Cohen-Macaulay normal domains and we compute the divisor class group and the canonical class. It allows us to determine which of our rings are Gorenstein. 相似文献
20.
The complemented ideals in the disk algebra are characterized. The projection operators onto the ideals and the complements
of the ideals are identified.
Research partially supported by a National Academy of Sciences Fellowship to the USSR during the 1977–78 academic year.
This author wishes to thank S. Khrushchev, V. Peller, S. Kisljakov, I. Vasoonin, and B. Mitiagin for their many helpful comments
and suggestions. 相似文献