Self-tilting complexes yield unstable modules

The paper is concerned with rings of polynomial invariants of finite groups. In particular, it will be shown that these rings are isomorphic as modules over the Steenrod algebra P* if and only if the group representations are pointwise conjugate. An application to cohomology is the construction of classifying spaces of finite groups which are not homotopy equivalent, but where the cohomology rings are isomorphic as unstable modules over the (topological) Steenrod algebra.

INTRODUCTION In the broadest sense, this is a study of commutative rings which satisfy the (finitely) pseudo-Froben[us (or (F)PF) condition: All (finitely generated) faithful modules generate the category mod-R of all R-modules. These rings include: Pr[[fer rings, almost maximal valuation rings, self-injective rings, e.g. , quasi-Frobenius (QF) and pseudo-Frobenius (PF) rings, and finite products of these. (In fact, any product of commutative FPF rings is FPF [34]; hence, any product of commutative PF rings is FPF (cf. §9).) If R is FPF, so is its (classical)ring of quotients Qc~(R) and its maximal quotient ring Qmax(R). All known FPF rings are (classically) quotientinjective in the sense that Qcf is injective. 2 We conjecture that all FIDF rings are quot[ent-injective, and prove this in the three cases: (i) local rings (Proposition 7 and Theorem 9B): (2) Noether[an rings (Theorem ii; Endo' s Theorem [25J~ (3) reduced rings (Proposition 3B and Theorem 4). Moreover, any FPF commutative ring R splits, R = R 1 X R2, where R 1 is semihered[tary, and R 2 has essential nilradical. (If R is semilocal or Noetherian, then R 2 is injective. ) Thus any reduced FPF ring has regular [njective Qc~' and conversely any quotient-injective sem[hered[tary ring is FPF (Theorem 4). A ring iS pre-(l~PF iff all(finitely generated)faithful ideals are generators, and we

Commutative Noetherian local rings whose ideals are direct sums of cyclic modules

Suppose that G is a finite group and k is a field of characteristic p > 0. A ghost map is a map in the stable category of finitely generated kG-modules which induces the zero map in Tate cohomology in all degrees. In an earlier paper we showed that the thick subcategory generated by the trivial module has no nonzero ghost maps if and only if the Sylow p-subgroup of G is cyclic of order 2 or 3. In this paper we introduce and study variations of ghost maps. In particular, we consider the behavior of ghost maps under restriction and induction functors. We find all groups satisfying a strong form of Freyd’s generating hypothesis and show that ghosts can be detected on a finite range of degrees of Tate cohomology. We also consider maps that mimic ghosts in high degrees.

Serial liver biopsies: a gateway into understanding the long-term health of the liver allograft

For a commutative local ring R, we know that every ideal is a direct sum of local modules if and only if the unique maximal ideal of R is of the form , where and are principal ideal rings and for all γ’s. This motivates us to determine a commutative ring, not necessarily local, in which every (proper) ideal is a direct sum of local modules. We prove that such a ring is exactly a finite direct product of local rings R with the unique maximal ideal in the above mentioned form. Moreover, we characterize more precisely certain commutative rings such as Noetherian rings, reduced rings, Rickart rings, semi-Artinian rings and self-injective rings, in which every (proper) ideal is a direct sum of local modules.

The cohomology ring away from 2 of configuration spaces on real projective spaces

Torsion theories over commutative rings

The work presented here is a continuation of that presented in an earlier paper, M. Rosenblatt and J. Van Ness [15], in which the basic properties (unbiasedness and consistency) of certain estimates of the bispectrum and bispectral density are discussed. (The bispectrum can be thought of as the Fourier transform of the third-order moment function of the process.) The present paper is concerned with the asymptotic distribution of these estimates. One would expect that under certain regularity conditions these estimates would have distributions which tend to complex normal distributions. The following develops two different sets of such conditions either of which suffice. The first set involves a uniform summability condition on the first six cumulants of a sequence of processes obtained from the original process by projecting it onto a certain sequence of Borel fields. The second, and much more intuitively meaningful, set involves the strong mixing condition (see Rosenblatt [11], [12]; Kolmogorov and Rozanov [6], and Volkonskii and Rozanov [18] e.g.). The calculations in the earlier paper were carried out for the continuous parameter case; here we restrict ourselves to the discrete parameter case. For reasons for interest in polyspectra see, for example, Rosenblatt and Van Ness [15]; Hasselmann, Munk and MacDonald [4]; and Brillinger [2].

Given an equivariant oriented cohomology theory $h$, a split reductive group $G$, a maximal torus $T$ in $G$, and a parabolic subgroup $P$ containing $T$, we explain how the $T$-equivariant oriented cohomology ring $h_T(G/P)$ can be identified with the dual of a coalgebra defined using exclusively the root datum of $(G,T)$, a set of simple roots defining $P$ and the formal group law of $h$. In two papers [Push-pull operators on the formal affine Demazure algebra and its dual, arXiv:1312.0019] and [A coproduct structure on the formal affine Demazure algebra, arXiv:1209.1676], we studied the properties of this dual and of some related operators by algebraic and combinatorial methods, without any reference to geometry. The present paper can be viewed as a companion paper, that justifies all the definitions of the algebraic objects and operators by explaining how to match them to equivariant oriented cohomology rings endowed with operators constructed using push-forwards and pull-backs along geometric morphisms. Our main tool is the pull-back to the $T$-fixed points of $G/P$ which injects the cohomology ring in question into a direct product of a finite number of copies of the $T$-equivariant oriented cohomology of a point.

In this paper we present a new approach to Grothendieck duality over commutative rings. Our approach is based on the idea of rigid dualizing complexes, which was introduced by Van den Bergh in the context of noncommutative algebraic geometry. The method of rigidity was modified to work over general commutative base rings in our paper (Yekutieli and Zhang, Trans AMS 360:3211-3248, 2008). In the present paper we obtain many of the important local features of Grothendieck duality, yet manage to avoid lengthy and difficult compatibility verifications. Our results apply to essentially finite type algebras over a regular noetherian finite dimensional base ring, and hence are suitable for arithmetic rings. In the sequel paper (Yekutieli, Rigid dualizing complexes on schemes, in preparation) these results will be used to construct and study rigid dualizing complexes on schemes.

For more than a century, the constructive description of functional classes in terms of the possible rate of approximation of its functions by means of functions chosen from a certain set remains among the most important problems of approximation theory. It turns out that the nonuniformity of the approximation rate due between the points of the domain of the approximated function is substantial. For instance, it was only in the mid-1950s that it was possible to constructively describe Holder classes on the segment [–1; 1] in terms of the approximation by algebraic polynomials. For that particular case, the constructive description requires the approximation at neighborhoods of the segment endpoints to be essentially better than the one in a neighborhood of its midpoint. A possible approximation quality test is to find out whether the approximation rate provides a possibility to reconstruct the smoothness of the approximated function. Earlier, we investigated the approximation of classes of smooth functions on a countable union of segments on the real axis. In the present paper, we prove that the rate of the approximation by the entire exponential-type functions provides the possibility to reconstruct the smoothness of the approximated function, i.e., a constructive description of classes of smooth functions is possible in terms of the specified approximation method. In an earlier paper, that result is announced for Holder classes, but the construction of a certain function needed for the proof is omitted. In the present paper, we use another proof; it does not apply the specified function.

Uniformidade da produção numa experiência de adubação da laranjeira baía

Unconventional monetary policy (UMP) influences inequality through two channels that work in opposite directions – a labour market channel (more employment, higher wages) and a financial market channel (higher asset prices). In an earlier paper, covering UMP through 2014, we found that UMP in Japan had contributed to greater income inequality through its effects on asset prices. With a longer time period, a richer dataset including labour market data, and a structural vector autoregression (SVAR) we confirm that these results continue to hold, and investigate why UMP’s impact on inequality in Japan differs from some other countries. We argue that Japanese structural issues may mute the labour market channel, especially: (i) labour market rigidity; and (ii) the large share of the population that is older than 65 years old or retired. The older cohort’s capital gains and dividends are re-saved in other financial assets, instead of being consumed or used for starting businesses. At the same time, wages have not increased despite the severe labour shortage, due to the frictions in Japan’s labour market. We conclude that these factors may make the inequality created by UMP in Japan unique by international comparison.

The only species of Cladocera so far known from Rajasthan is Latona tiwari decribed by BISwAS (1964) . The present paper which deals with 17 species of Cladocera, is based on a few collections from different localities in Raj asthan during the period between 1962 and 1964. In earlier papers I have already described the Conchostraca (NAYAR, 1965) and Rotifera (NAYAR, 1968) present in those collections .