共查询到20条相似文献，搜索用时 15 毫秒
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Gianfranco Casnati 《代数通讯》2013,41(8):2738-2761
Let k be an algebraically closed field of characteristic 0. We give here a complete classification of local commutative, associative, Artinian, Gorenstein k-algebras with unit, up to multiplicity 9. 相似文献
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The study of the h-vectors of graded Gorenstein algebras is an important topic in combinatorial commutative algebra, which despite the large amount of literature produced during the last several years, still presents many interesting open questions. In this note, we commence a study of those unimodal Gorenstein h-vectors that do not satisfy the Stanley–Iarrobino property. Our main results, which are characteristic free, show that such h-vectors exist: 1) In socle degree e if and only if e≥6; and 2) in every codimension five or greater. The main case that remains open is that of codimension four, where no Gorenstein h-vector is known without the Stanley–Iarrobino property. We conclude by proposing the following very general conjecture: The existence of any arbitrary level h-vector is independent of the characteristic of the base field. 相似文献
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Fabrizio Zanello 《Transactions of the American Mathematical Society》2007,359(6):2675-2686
Given a vector space of homogeneous polynomials of the same degree over an infinite field, consider a generic subspace of . The main result of this paper is a lower-bound (in general sharp) for the dimensions of the spaces spanned in each degree by the partial derivatives of the forms generating , in terms of the dimensions of the spaces spanned by the partial derivatives of the forms generating the original space . This result generalizes a recent theorem of Iarrobino (which treats the case ).
Rephrasing our result in the language of commutative algebra (where this result finds its most important applications), we have: let be a type artinian level algebra with -vector , and let, for , be the -vector of the generic type level quotient of having the same socle degree . Then we supply a lower-bound (in general sharp) for the -vector . Explicitly, we will show that, for any ,
Finally, we begin to obtain, as a consequence, some structure theorems for level -vectors of type bigger than 2, which is, at this time, a very little explored topic.
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Jan O. Kleppe 《Transactions of the American Mathematical Society》2006,358(7):3133-3167
The purpose of this paper is to study maximal irreducible families of Gorenstein quotients of a polynomial ring . Let be the scheme parametrizing graded quotients of with Hilbert function . We prove there is a close relationship between the irreducible components of , whose general member is a Gorenstein codimension quotient, and the irreducible components of , whose general member is a codimension Cohen-Macaulay algebra of Hilbert function related to . If the Castelnuovo-Mumford regularity of the Gorenstein quotient is large compared to the Castelnuovo-Mumford regularity of , this relationship actually determines a well-defined injective mapping from such ``Cohen-Macaulay' components of to ``Gorenstein' components of , in which generically smooth components correspond. Moreover the dimension of the ``Gorenstein' components is computed in terms of the dimension of the corresponding ``Cohen-Macaulay' component and a sum of two invariants of . Using linkage by a complete intersection we show how to compute these invariants. Linkage also turns out to be quite effective in verifying the assumptions which appear in a generalization of the main theorem.
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Xinhong Chen 《代数通讯》2017,45(2):849-865
For any skewed-gentle algebra, we characterize its indecomposable Gorenstein projective modules explicitly and describe its Cohen–Macaulay Auslander algebra. We prove that skewed-gentle algebras are always Gorenstein, which is independent of the characteristic of the ground field, and the Cohen–Macaulay Auslander algebras of skewed-gentle algebras are also skewed-gentle algebras. 相似文献
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Sabine El Khoury 《代数通讯》2013,41(9):3259-3277
In this article, we study height four graded Gorenstein ideals I in k[x, y, z, w] such that I 2 is of height one and generated by three quadrics. After a suitable linear change of variables, I ∩ k[x, y, z] is either Gorenstein or of type two. The former case was studied by Iarrobino and Srinivasan [8] where they give the structure of the ideal and its resolution. We study the latter case and give the structure of these ideals and their minimal resolution. We also explicitly write the form of the generators of I and the maps in the free resolution of R/I. 相似文献
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Fabrizio Zanello 《代数通讯》2013,41(4):1087-1091
The purpose of this note is to supply an upper and a lower bound (which are in general sharp) for the h-vector of a level algebra which is relatively compressed with respect to any arbitrary level algebra A. The useful concept of relatively compressed algebra was recently introduced in Migliore et al. (2005) (whose investigations mainly focused on the particular case of A a complete intersection). The key idea of this note is the simple observation that the level algebras which are relatively compressed with respect to A coincide (after an obvious isomorphism) with the generic level quotients of suitable truncations of A. Therefore, we are able to apply to relatively compressed algebras the main result of our recent work, Zanello (2007). 相似文献
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We prove that any quasiassociative algebra with simple Artinian null part is isomorphic to a unique matrix algebra Mn(), where is a quasiassociative division algebra. 相似文献
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A new class of Gorenstein algebras T m,n (A) is introduced, their module categories are described, and all the Gorenstein-projective T m,n (A)-modules are explicitly determined. 相似文献
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令H是有限维Hopf代数，A是左H-模代数。本文证明了A是Gorenstein代数的充分必要条件。A^H也是Gorenstein代数的条件。它是Enochs EE,GarciaJJ和del RioA关于群作用相应的理论的推广，同时给出A/A^H是Frobenius扩张的条件。 相似文献
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Brian A. Coolen 《代数通讯》2013,41(5):1595-1612
Given a compressed Artin level algebra A which satisfies certain properties, it is possible to use this algebra to construct a Gorenstein Artin algebra with a nonunimodal Hilbert function. We show how to construct a minimal free resolution for these algebras, using the minimal free resolution of A. 相似文献
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Junzo Watanabe 《Proceedings of the American Mathematical Society》1998,126(11):3161-3168
Let be a field of characteristic 0. If is a complete intersection generated by three homogeneous elements of degrees with , then the reduction of by a general linear form is minimally generated by three elements if and only if .