نتایج جستجو برای: artinian

تعداد نتایج: 593  

2001
J. MIGLIORE U. NAGEL

An SI-sequence is a finite sequence of positive integers which is symmetric, unimodal and satisfies a certain growth condition. These are known to correspond precisely to the possible Hilbert functions of Artinian Gorenstein algebras with the Weak Lefschetz Property, a property shared by most Artinian Gorenstein algebras. Starting with an arbitrary SI-sequence, we construct a reduced, arithmeti...

Journal: :CoRR 2017
Friedrich Martin Schneider Jens Zumbrägel

Finite Frobenius rings have been characterized as precisely those finite rings satisfying the MacWilliams extension property, by work of Wood. In the present note we offer a generalization of this remarkable result to the realm of Artinian rings. Namely, we prove that a left Artinian ring has the left MacWilliams property if and only if it is left pseudo-injective and its finitary left socle em...

2012
Faisal Hassany

Let R = ⊕ n∈N0 Rn be a Noetherian homogeneous ring with local base ring (R0,m0) and irrelevant ideal R+, let M be a finitely generated graded R− module. In this paper we show that if R0 is a local ring of dimension one, then H i R+(H 1 m0R (M)) is Artinian for each i ∈ N0. Let f be the least integer such that H i m0R(M) is not finitely generated graded R−module. In this case, we prove that ΓR+(...

The paper uses a new approach to investigate prime submodules and minimal prime submodules of certain modules such as Artinian and torsion modules. In particular, we introduce a concrete formula for the radical of submodules of Artinian modules.

2005
YONG SU SHIN

It is unknown if an Artinian level O-sequence of codimension 3 and type r (≥ 2) is unimodal, while it is known that any Gorenstein O-sequence of codimension 3 is unimodal. We show that some Artinian non-unimodal O-sequence of codimension 3 cannot be level. We also find another non-level case: if some Artinian algebra A of codimension 3 has the Hilbert function H : h0 h1 · · · hd−1 hd · · · hd }...

2006
THOMAS J. DORSEY

We observe that the class of left and right artinian left and right morphic rings agrees with the class of artinian principal ideal rings. For R an artinian principal ideal ring and G a group, we characterize when RG is a principal ideal ring; for finite groups G, this characterizes when RG is a left and right morphic ring. This extends work of Passman, Sehgal and Fisher in the case when R is a...

Journal: :Canadian Mathematical Bulletin 2011

2017
Joost Berson

In a recent paper it has been established that over an Artinian ring R all two-dimensional polynomial automorphisms having Jacobian determinant one are tame if R is a Q-algebra. This is a generalization of the famous Jung-Van der Kulk Theorem, which deals with the case that R is a field (of any characteristic). Here we will show that for tameness over an Artinian ring, the Q-algebra assumption ...

2005
J. Cuadra J. Gómez-Torrecillas

The Jacobson-Bourbaki Theorem for division rings was formulated in terms of corings by Sweedler in [14]. Finiteness conditions hypotheses are not required in this new approach. In this paper we extend Sweedler’s result to simple artinian rings using a particular class of corings, comatrix corings. A Jacobson-Bourbaki like correspondence for simple artinian rings is then obtained by duality.

2009
TOSHIAKI MAENO JUNZO WATANABE

We give a characterization of the Lefschetz elements in Artinian Gorenstein rings over a field of characteristic zero in terms of the higher Hessians. As an application, we give new examples of Artinian Gorenstein rings which do not have the strong Lefschetz property.

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