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1.
We consider pomonoids
, where G is a pogroup and I is a poideal of S and show that if an S-poset is principally weakly flat, (weakly) flat, po-flat, (principally) weakly po-flat, (po-) torsion free or satisfies Conditions
(P), (P
E
), (P
w
), (PWP), (PWP)
w
, (WP) or (WP)
w
as an I
1-poset, then it has these properties as an S-poset. We also show that an S-poset which is free, projective or strongly flat as an I
1-poset may not generally have these properties as an S-poset. 相似文献
2.
Monoids over which all flat cyclic right acts are strongly flat 总被引:2,自引:0,他引:2
3.
If S is a monoid, the right S-act S×S, equipped with componentwise S-action, is called the diagonal act of
S. The question of when this act is cyclic or finitely generated has been a subject of interest for many years, but so far
there has been no explicit work devoted to flatness properties of diagonal acts. Considered as a right S-act, the monoid S is free, and thus is also projective, flat, weakly flat, and so on. In 1991, Bulman-Fleming gave conditions on S under which all right acts S
I
(for I a non-empty set) are projective (or, equivalently, when all products of projective right S-acts are projective). At approximately the same time, Victoria Gould solved the corresponding problem for strong flatness.
Implicitly, Gould’s result also answers the question for condition (P) and condition (E). For products of flats, weakly flats,
etc. to again have the same property, there are some published results as well. The specific questions of when S×S has certain flatness properties have so far not been considered. In this paper, we will address these problems.
S. Bulman-Fleming research supported by Natural Sciences and Engineering Research Council of Canada Research Grant A4494.
Some of the results in this article are contained in the M.Math. thesis of A. Gilmour, University of Waterloo (2007). 相似文献
4.
Akbar Golchin 《Semigroup Forum》2005,70(2):296-301
We consider monoids $S=G\;\dot{\cup}\; I$ where $G$ is a group and $I$ is an ideal of $S$ and show that if an $S$-act is principally
weakly homoflat or weakly homoflat as an $I^1$-act, then it has
these properties as an $S$-act. We also show that an $S$-act which
is (weakly) pullback flat, equalizer flat, (principally) weakly
kernel flat, translation kernel flat or satisfies Condition $(E)$
as an $I^1$-act may not generally have these properties as an
$S$-act. The flatness notions considered in this paper were
introduced in {\it V. Laan, Pullbacks and flatness properties of
acts I, Comm. Alg. ${\bf 29}(2)$ (2001), 829--850}. 相似文献
5.
Marc Levine 《K-Theory》1992,6(2):113-175
LetR be a commutative, semi-local ring,I
1, ...,I
s
ideals. In this paper, we define therelative Milnor K-groups of (R;I
1, ...,I
s
),K
p
M
(R;I
1, ...,I
s
), and show that these groups have many of the properties of the usual MilnorK-groups of a field. In particular, assuming a weak condition on the ideals, we show thatK
p
M
(R;I
1, ...,I
s
) is isomorphic to the weightp portion of the relative QuillenK-groupK
p
(R;I
1, ...,I
s
), after inverting (p–1)!. We also define the relative group homology of GL
n
(R;I
1, ...,I
s
), and show thatK
p
M
(R;I
1, ...,I
s
) is isomorphic toH
p
(GLp(R;I
1, ...,I
s
))/Im(H
p
(GL
p–1 (R;I
1, ...,I
s
))). Finally, we consider a generalization to the relative setting of Kato's conjecture asserting that the Galois symbol gives an isomorphism fromK
p
M
(F)/l
v
to
, and show that this relative version of Kato's conjecture implies the Quillen-Lichtenbaum conjectures asserting the Chern class:
相似文献
6.
M. M. Popov 《Archiv der Mathematik》2008,90(6):537-544
The well known Daugavet property for the space L
1 means that || I + K || = 1+ || K || for any weakly compact operator K : L
1 → L
1, where I is the identity operator in L
1. We generalize this theorem to the case when we consider an into isomorphism J : L
1 → L
1 instead of I and a narrow operator T. Our main result states that , where d = || J|| || J
−1||. We also give an example which shows that this estimate is exact.
Received: 21 August 2007 相似文献
7.
Dr. Johannes Schoißengeier 《Monatshefte für Mathematik》1979,87(4):313-316
LetI=[0,1),dω the product measure onI ? of the Lebesgue measure onI, D N (ω) the discrepancy ofω ∈I ?. We show that for α>0 $$\mathop {\lim }\limits_{N \to \infty } N^{\alpha /2} \mathop \smallint \limits_{I^\mathbb{N} } D_N^\alpha (\omega ) d\omega = 4.2 - (3\alpha /2)(2\alpha - 1 - 1) \zeta (\alpha ) \Gamma (\alpha /2 + 1)$$ Furthermore we sharpen and generalize this result. 相似文献
8.
Let {(Xi,|| · || i)}i ? I,\{(X_i,\left \| {\cdot } \right \| _{i})\}_{i\in I}, be an arbitrary family of normed spaces and let (E,|| · || E)(E,\left \| {\cdot } \right \| _{E}) be a monotonic normed space of real functions on the set I that is an ideal in \Bbb RI{\Bbb R}^I. We prove a sufficient condition for the direct sum space E(Xi) to be uniformly rotund in a direction. We show that this condition is also necessary for E=l¥E=\ell _{\infty }, and it is not necessary for E=l1E=\ell _1. When E is either uniformly rotund in every direction and has compact order intervals, or weakly uniformly rotund respect to its evaluation functionals, we reestablish as a corollary the result that reads: E(Xi)E(X_i) is uniformly rotund in every direction if and only if so are all the Xi. 相似文献
9.
Pan Wenjie 《分析论及其应用》1992,8(1):1-15
We study fractional integrals on spaces of homogeneous type defined byI α f(x)=∫Xf(y)|B(x,d(x,y))|ga?1dμ(y), 0<α<1. If \(1< p\frac{1}{\alpha },\frac{1}{q} = \frac{1}{p} - \alpha \) , we show that Iαf is of strong type (p,q) and is of weak type ( \(\left( {1,\frac{1}{{1 - \alpha }}} \right)\) ). We also consider the necessary and sufficient conditions on two weights for which Iαf is of weak type (p,q) with respect to (w,v). 相似文献
10.
The study of the free idempotent generated semigroup IG(E) over a biordered set E has recently received a deal of attention. Let G be a group, let \(n\in\mathbb{N}\) with n≥3 and let E be the biordered set of idempotents of the wreath product \(G\wr \mathcal{T}_{n}\) . We show, in a transparent way, that for e∈E lying in the minimal ideal of \(G\wr\mathcal{T}_{n}\) , the maximal subgroup of e in IG(E) is isomorphic to G. It is known that \(G\wr\mathcal{T}_{n}\) is the endomorphism monoid End F n (G) of the rank n free G-act F n (G). Our work is therefore analogous to that of Brittenham, Margolis and Meakin for rank 1 idempotents in full linear monoids. As a corollary we obtain the result of Gray and Ru?kuc that any group can occur as a maximal subgroup of some free idempotent generated semigroup. Unlike their proof, ours involves a natural biordered set and very little machinery. 相似文献
11.
12.
The fractional Laplacian
(-\triangle)g/2(-\triangle)^{\gamma/2} commutes with the primary coordination transformations in the Euclidean space ℝ
d
: dilation, translation and rotation, and has tight link to splines, fractals and stable Levy processes. For 0 < γ < d, its inverse is the classical Riesz potential I
γ
which is dilation-invariant and translation-invariant. In this work, we investigate the functional properties (continuity,
decay and invertibility) of an extended class of differential operators that share those invariance properties. In particular,
we extend the definition of the classical Riesz potential I
γ
to any non-integer number γ larger than d and show that it is the unique left-inverse of the fractional Laplacian
(-\triangle)g/2(-\triangle)^{\gamma/2} which is dilation-invariant and translation-invariant. We observe that, for any 1 ≤ p ≤ ∞ and γ ≥ d(1 − 1/p), there exists a Schwartz function f such that I
γ
f is not p-integrable. We then introduce the new unique left-inverse I
γ, p
of the fractional Laplacian
(-\triangle)g/2(-\triangle)^{\gamma/2} with the property that I
γ, p
is dilation-invariant (but not translation-invariant) and that I
γ, p
f is p-integrable for any Schwartz function f. We finally apply that linear operator I
γ, p
with p = 1 to solve the stochastic partial differential equation
(-\triangle)g/2 F = w(-\triangle)^{\gamma/2} \Phi=w with white Poisson noise as its driving term w. 相似文献
13.
In this article we characterize monoids over which every right S-act has a strongly flat (condition (P)) cover. Similar to the perfect monoids, such monoids are characterized by condition (A) and having strongly flat (condition (P)) cover for each cyclic right S-act. We also give a new characterization for perfect monoids as monoids over which every strongly flat right S-act has a projective cover. 相似文献
14.
A. Cordón‐Franco A. Fernández‐Margarit F. F. Lara‐Martín 《Mathematical Logic Quarterly》2011,57(5):444-455
We characterize the sets of all Π2 and all $\mathcal {B}(\Sigma _{1})
15.
We shall call a monoid S principally weakly (weakly) left coherent if direct products of nonempty families of principally weakly (weakly) flat right S-acts are principally weakly (weakly) flat. Such monoids have not been studied in general. However, Bulman-Fleming and McDowell proved that a commutative monoid S is (weakly) coherent if and only if the act S I is weakly flat for each nonempty set I. In this article we introduce the notion of finite (principal) weak flatness for characterizing (principally) weakly left coherent monoids. Also we investigate monoids over which direct products of acts transfer an arbitrary flatness property to their components. 相似文献
16.
E. Gečiauskas 《Geometriae Dedicata》2006,121(1):9-18
We have obtained a recurrence formula $I_{n+3} = \frac{4(n+3)}{\pi(n+4)}VI_{n+1}
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