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1.
ABSTRACT We find representatives of all the equivalence classes of simple root systems (or r.e.s. for brevity) for the complex reflection groups G 12 , G 24 , G 25 and G 26 . Then we give representatives of all the congruence classes of (essential) presentations (or r.c.p. (r.c.e.p.) for brevity) for these groups by generators and relations. The method used in the paper is applicable to any finite (complex) reflection groups. 相似文献
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Weimin Xue 《中国科学A辑(英文版)》1998,41(12):1233-1240
Two theorems are established which properly extend the ckss of artinian rings with Morita duality. A question of Anh about
QF-rings is answered in the negative.
Project supported by the National Natural Science Foundation of China (Grant No. 19771016). 相似文献
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In this paper Morita duality for monoids is introduced. Necessary and sufficient conditions for two monoids S and T to be
Morita dual are given. Moreover, it is shown that if S and T are Morita dual monoids, then S and U are Morita dual if and
only if T and U are Morita equivalent. In addition, every finite monoid having Morita duality is selfdual and even reflexive. 相似文献
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Algebras and Representation Theory - It is shown that a general concept of Morita duality between abelian categories with no generating hypothesis for reflexive objects is completely described by a... 相似文献
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In this paper, weak distinguished subcategory and distinguished subcategory of modules are introduced. Left(right) local unital rings are particularly considered. Also, representable equivalent functors between categories. By using the replacement techniques of modules, a general theory of Morita equivalence for infinite matrix rings is established. This theory not only extends the classical Morita theory of equivalence from finite matrix rings to infinite matrix rings and also contains some new results which are useful in studying the algebraic structures for infinite matrix rings. Some results of classical Morita theory are included as its special cases. 相似文献
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Associated to any simplicial complex Δ on n vertices is a square-free monomial ideal IΔ in the polynomial ring A = k[x1, …, xn], and its quotient k[Δ] = A/IΔ known as the Stanley-Reisner ring. This note considers a simplicial complex Δ* which is in a sense a canonical Alexander dual to Δ, previously considered in [1, 5]. Using Alexander duality and a result of Hochster computing the Betti numbers dimk ToriA (k[Δ],k), it is shown (Proposition 1) that these Betti numbers are computable from the homology of links of faces in Δ*. As corollaries, we prove that IΔ has a linear resolution as A-module if and only if Δ* is Cohen-Macaulay over k, and show how to compute the Betti numbers dimk ToriA (k[Δ],k) in some cases where Δ* is wellbehaved (shellable, Cohen-Macaulay, or Buchsbaum). Some other applications of the notion of shellability are also discussed. 相似文献
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Let be a Morita ring, where the bimodule homomorphisms and are zero. We study the finite presentedness, locally coherence, pure projectivity, pure injectivity, and FP-injectivity of modules over . Some applications are then given. 相似文献
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A. Haghany 《Periodica Mathematica Hungarica》1996,32(3):193-197
We generalize the well-known fact that for a pair of Morita equivalent ringsR andS their maximal rings of quotients are again Morita equivalent: If
n
(M) denotes the torsion theory cogenerated by the direct sum of the firstn+1 injective modules forming part of the minimal injective resolution ofM then
n
(R)=
n
(S) where is the category equivalenceR-ModS-Mod. Consequently the localized ringsR
n
(R) andS
n
(S) are Morita equivalent. 相似文献
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Joel K. Haack 《代数通讯》2013,41(19):2107-2119
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We prove that a stable equivalence of Morita type between finite dimensional algebras preserves the stable Hochschild cohomology
rings, that is, Hochschild cohomology rings modulo the projective center, thus generalizing the results of Pogorzały and Xi. 相似文献
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Claudia Menini 《代数通讯》2013,41(9):1779-1797
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Tzu-Chun Lin 《Proceedings of the American Mathematical Society》2006,134(6):1599-1604
Let be a faithful representation of a finite group over the field . Via the group acts on and hence on the algebra of homogenous polynomial functions on the vector space . R. Kane (1994) formulated the following result based on the work of R. Steinberg (1964): If the field has characteristic 0, then is a Poincaré duality algebra if and only if is a pseudoreflection group. The purpose of this note is to extend this result to the case (i.e. the order of is relatively prime to the characteristic of ).
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Laszlo Fuchs 《Annali di Matematica Pura ed Applicata》1978,117(1):227-232
Sunto. Rispondendo ad una questione posta da A. Orsatti in[8], si dà esempio di dualità, non soddisfacente alle proprietà di estensione di caratteri, sopra un anello di valutazione discreto
completo e si ottiene una caratterizzazione dei domini noetheriani per cui una tale dualità esiste.
Entrata in Redazione il 17 maggio 1977.
This paper has been written while the author was visiting professor in Dept. of Mathematics of Università di Padova. 相似文献
Entrata in Redazione il 17 maggio 1977.
This paper has been written while the author was visiting professor in Dept. of Mathematics of Università di Padova. 相似文献
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Ikuo Nishitani 《代数通讯》2013,41(7):2669-2676
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Let L be a graded Lie algebra of Cartan type over an algebraically closed field of characteristic p≧3, which has been proved to be generalized restricted in the sense of [Shul, Shu2]. For a generalized restricted L-module M, the homological support variety ‖L‖M is defined to be that of the primitive p-envelope P{L). A realization L of P(L) is given in Der(&;(m : n)). Furthermore, a class of generalized restricted highest weight L-modules lift to Dist(Tx)V(p)-module structures and their support varieties can be computed by using algebraic group techniques developed in [LN]. 相似文献