658 research outputs found
Topics on -almost Gorenstein rings
The notion of -almost Gorenstein ring is a generalization of the notion of
almost Gorenstein ring in terms of Sally modules of canonical ideals. In this
paper, we deal with two different topics related to -almost Gorenstein
rings. The purposes are to determine all the Ulrich ideals in -almost
Gorenstein rings and to clarify the structure of minimal free resolutions of
-almost Gorenstein rings.Comment: 12 page
Almost Gorenstein rings arising from fiber products
The purpose of this paper is, as part of the stratification of Cohen-Macaulay
rings, to investigate the question of when the fiber products are almost
Gorenstein rings. We show that the fiber product of
Cohen-Macaulay local rings , of the same dimension over a regular
local ring with is an almost Gorenstein ring if and only if so
are and . Besides, the other generalizations of Gorenstein properties
are also explored.Comment: 15 page
Almost Gorenstein rings - towards a theory of higher dimension -
The notion of almost Gorenstein local ring introduced by V. Barucci and R.
Fr\"oberg for one-dimensional Noetherian local rings which are analytically
unramified has been generalized by S. Goto, N. Matsuoka and T. T. Phuong to
one-dimensional Cohen-Macaulay local rings, possessing canonical ideals. The
present purpose is to propose a higher-dimensional notion and develop the basic
theory. The graded version is also posed and explored.Comment: 36 pages, 1 figure, to appear in J. Pure and Appl. Al
On the ideal case of a conjecture of Huneke and Wiegand
A conjecture of Huneke and Wiegand claims that, over one-dimensional
commutative Noetherian local domains, the tensor product of a finitely
generated, non-free, torsion-free module with its algebraic dual always has
torsion. Building on a beautiful result of Corso, Huneke, Katz and Vasconcelos,
we prove that the conjecture is affirmative for a large class of ideals over
arbitrary one-dimensional local domains. Furthermore we study a higher
dimensional analog of the conjecture for integrally closed ideals over
Noetherian rings that are not necessarily local. We also consider a related
question on the conjecture and give an affirmative answer for first syzygies of
maximal Cohen-Macaulay modules.Comment: 10 pages and to appear in Proceedings of the Edinburgh Mathematical
Societ
Characterization of generalized Gorenstein rings
The notion of generalized Gorenstein local ring (GGL ring for short) is one
of the generalizations of Gorenstein rings. In this article, there is given a
characterization of GGL rings in terms of their canonical ideals and related
invariants.Comment: 11 page
Efficient generation of ideals in core subalgebras of the polynomial ring k[t] over a field k
This note aims at finding explicit and efficient generation of ideals in
subalgebras of the polynomial ring ( a field) such that
for some integer . The class of these
subalgebras which we call cores of includes the semigroup rings of
numerical semigroups , but much larger than the class of numerical semigroup
rings. For and , our result eventually
shows that where (resp. )
stands for the minimal number of generators of (resp. ), which covers in
the specific case the classical result of O. Forster-R. G. Swan.Comment: 10 page
The almost Gorenstein Rees algebras of parameters
There is given a characterization for the Rees algebras of parameters in a
Gorenstein local ring to be almost Gorenstein graded rings. A characterization
is also given for the Rees algebras of socle ideals of parameters. The latter
one shows almost Gorenstein Rees algebras rather rarely exist for socle ideals,
if the dimension of the base local ring is greater than two.Comment: 13 page
Almost Gorenstein Rees algebras of -ideals, good ideals, and powers of the maximal ideals
Let be a Cohen-Macaulay local ring and let be an
ideal of . We prove that the Rees algebra is an almost
Gorenstein ring in the following cases: (1) is a
two-dimensional excellent Gorenstein normal domain over an algebraically closed
field and is a -ideal; (2) is a two-dimensional almost Gorenstein local ring having minimal
multiplicity and for all ; (3)
is a regular local ring of dimension and
. Conversely, if is
an almost Gorenstein graded ring for some and , then
.Comment: 14 pages, and the title of this article was changed on 26, June, 201
When are the Rees algebras of parameter ideals almost Gorenstein graded rings?
Let be a Cohen-Macaulay local ring with ,
possessing the canonical module . Let
be a subsystem of parameters of and set . It is shown that if the Rees algebra of is
an almost Gorenstein graded ring, then is a regular local ring and is a part of a regular system of parameters of .Comment: 9 page
On the almost Gorenstein property in Rees algebras of contracted ideals
The question of when the Rees algebra of is an almost Gorenstein graded ring is explored, where is a
two-dimensional regular local ring and a contracted ideal of . It is
known that is an almost Gorenstein graded ring for every
integrally closed ideal of . The main results of the present paper show
that if is a contracted ideal with , then is an almost Gorenstein graded ring, while if ,
then is not necessarily an almost Gorenstein graded ring,
even though is a contracted stable ideal. Thus both affirmative answers and
negative answers are given.Comment: 15 page
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