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1.
We develope the theory of \({\mathcal {E}}\)-relative Igusa-Todorov functions in an exact I T-context \(({\mathcal {C}},{\mathcal {E}})\) (see Definition 2.1). In the case when \({\mathcal {C}}={\text {mod}}\, ({\Lambda })\) is the category of finitely generated left Λ-modules, for an artin algebra Λ, and \({\mathcal {E}}\) is the class of all exact sequences in \({\mathcal {C}},\) we recover the usual Igusa-Todorov functions, Igusa K. and Todorov G. (2005). We use the setting of the exact structures and the Auslander-Solberg relative homological theory to generalise the original Igusa-Todorov’s results. Furthermore, we introduce the \({\mathcal {E}}\)-relative Igusa-Todorov dimension and also we obtain relationships with the relative global and relative finitistic dimensions and the Gorenstein homological dimensions. 相似文献
2.
Mathematical Notes - Structure properties of multiplicatively idempotent semirings are considered. Basic results concerning completely prime ideals in multiplicatively idempotent semirings are... 相似文献
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Mathematical Notes - For a wide class of algebras P of holomorphic functions on a domain in ?, sufficient conditions are obtained under which a closed ideal I ? P is 2-generated. 相似文献
5.
Let R be a homogeneous ring over an infinite field, IR a homogeneous ideal, and
I an ideal generated by s forms of degrees d
1,...,d
s
so that codim(
:I)s. We give broad conditions for when the Hilbert function of R/
or of R/(
:I) is determined by I and the degrees d
1,...,d
s
. These conditions are expressed in terms of residual intersections of I, culminating in the notion of residually S
2 ideals. We prove that the residually S
2 property is implied by the vanishing of certain Ext modules and deduce that generic projections tend to produce ideals with this property. 相似文献
6.
Let E be a ring of entire functions on
with the operation of pointwise multiplication, and let f
1,...,f
m
be a set of nonzero elements in E. The ideal E(f
1,...,f
m
) in E with generators f
1,...,f
m
is said to be generating if E(f
1,...,f
m
) = E. The generating ideals in rings of entire functions on
determined by the growth of their maximum moduli are characterized in terms of the distribution of the zero sets of their generators. Under the additional condition of rapid variation of the weight sequences determining the ring, criteria for generating ideals are established; they are stated in terms of d(z) max 1 j m
d
j
(z), where d
j
(z) is the distance from a point
to the zero set of f
j
for 1 j m. It is shown that, in rings of entire functions of finite or minimal type with respect to a given order, a similar characterization (i.e., in terms of d(z)) cannot be given. 相似文献
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8.
We study ideals in the space of entire functions of finite order and type on the plane. We obtain necessary and sufficient conditions for the ideal of functions vanishing at the common zeros of a system of N functions to be generated by the latter. 相似文献
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This article investigates the soft-interior (se) and the soft-cover (sc) of operator ideals. These operations, and especially
the first one, have been widely used before, but making their role explicit and analyzing their interplay with the arithmetic
mean operations is essential for the study in [10] of the multiplicity of traces. Many classical ideals are ‘soft’, i.e.,
coincide with their soft interior or with their soft cover, and many ideal constructions yield soft ideals. Arithmetic mean
(am) operations were proven to be intrinsic to the theory of operator ideals in [6, 7] and arithmetic mean operations at infinity
(am-∞) were studied in [10]. Here we focus on the commutation relations between these operations and soft operations. In the
process we characterize the am-interior and the am-∞ interior of an ideal.
Both authors were partially supported by grants of the Charles Phelps Taft Research Center; the second named author was partially
supported by NSF Grants DMS 95-03062 and DMS 97-06911. 相似文献
12.
Mathematical Notes - 相似文献
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Let X be a completely regular Hausdorff space, A be a unital locally convex algebra with jointly continuous multiplication and C(X,A) be the algebra of all continuous A-valued functions on X equipped with the topology of \({\mathcal{K}(X)}\) -convergence. Moreover, let \({\mathfrak{M}_{\ell}(A)}\) and \({\mathfrak{M}(A)}\) denote the set of all closed maximal left and two-sided ideals in A, respectively. In this note, we describe all closed maximal left and two-sided ideals in C(X,A) and show that there exist bijections from \({\mathfrak{M}_{\ell}(C(X, A))}\) onto \({X \times \mathfrak{M}_{\ell}(A)}\) and \({\mathfrak{M}(C(X, A))}\) onto \({X \times \mathfrak{M}(A)}\) . We also present new characterizations of closed maximal ideals in C(X, A) when A is a unital commutative locally convex Gelfand–Mazur algebra with jointly continuous multiplication. 相似文献
15.
A semigroup with zero isidempotent bounded (IB) if it is the 0-direct union of idempotent generated principal left ideals and the 0-direct union of idempotent generated principal right ideals. Notable examples are completely 0-simple semigroups and the wider class of primitive abundant semigroups. Significant to the structure of these semigroups is that they are all categorical at zero. In this paper we describe IB semigroups that are categorical at zero in terms ofdouble blocked Rees matrix semigroups. This generalises Fountain's characterisation of primitive abundant semigroups via blocked Rees matrix semigroups [1], which in turn yields the Rees theorem for completely 0-simple semigroups. 相似文献
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Idempotent Modules in the Stable Category 总被引:3,自引:0,他引:3
Let G be a finite group and k be an algebraically closed fieldof prime characteristic. Corresponding to each closed homogeneoussubvariety W of the maximal ideal spectrum of H*(G, k) we construct(usually infinite-dimensional) kG-modules E(W) and F(W) whichare idempotent in the sense that E(W) and F(W) are isomorphic(up to projective summands) to E(W) E(W) and F(W) F(W) respectively.We study the properties of these modules, and as an applicationwe use them to describe natural direct sum decompositions ofmodules in quotient categories. 相似文献
18.
Let S be a cancellation torsion-free additive semigroup with identity 0 and let S {0}. We consider the relation between the valuation ideals and primary ideals of S. We give a characterization that each primary ideal is a valuation ideal in S and also give a characterization that each valuation ideal is a primary ideal in S.AMS Subject Classification (1991): 20M14 相似文献
19.
L. B. Beasley A. E. Guterman K.-T. Kang S.-Z. Song 《Journal of Mathematical Sciences》2008,152(4):456-468
We obtain a new structural characterization of idempotent Boolean matrices. This characterization allows us to describe all Boolean matrices that are majorized by a given idempotent. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 1, pp. 11–29, 2007. 相似文献
20.
Dr. A. Mukherjea 《Probability Theory and Related Fields》1969,11(2):142-146
Summary In this paper, idempotent probability measures have been considered on semigroups which are locally compact or metric and satisfy: (*) A
–1
B and Ax
–1 are compact whenever A and B are so, for every x in the semigroup. Such semigroups are more general than compact semigroups which do admit of such measures. On such semigroups we can construct such measures by the usual process if there is a compact sub-semigroup. It is shown in this paper that if such a measure exists in such semigroups, then it must be such an extension measure. Some related results concerning the conditions (*) are also discussed here. 相似文献