704 research outputs found
A counterexample to a conjecture of Ding
We give a counterexample to a conjecture posed by S. Ding regarding the index
of a Gorenstein local ring by exhibiting several examples of one dimensional
local complete intersections of embedding dimension three with index 5 and
generalized L\"oewy length 6.Comment: 9 pages, a few changes from the first versio
Products of ideals may not be Golod
We exhibit an example of a product of two proper monomial ideals such that
the residue class ring is not Golod. We also discuss the strongly Golod
property for rational powers of monomial ideals, and introduce some sufficient
conditions for weak Golodness of monomial ideals. Along the way, we ask some
related questions.Comment: 18 pages, minor changes from first versio
Price Transmission in Three Italian Food Chains: A Structural Break Approach
Recently a wide instability of food prices has been observed in world and European agricultural and food markets. Both media and policy makers have dealt with the unsatisfactory patterns of marketing margins and price transmission along the food chain which may bring about distributive issues and affect inflationary trends. Although price transmission and margins dynamics have attracted so much interest at the policy level, few Italian studies deal with this topic. Our aim is to provide a first analysis of the price transmission mechanism in three Italian agri-food chains (lamb, pork and pasta), within a structural change framework. Results show that structural breaks in the price transmission mechanism are an issue in the food chain of pasta and pork with the regime change arising in occasion of the price bubble of 2007-2008.price transmission, cointegration, structural breaks, Agribusiness, Q13, L11,
A sufficient condition for strong -regularity
Let be an -finite Noetherian local ring which has a
canonical ideal . We prove that if is and
is a simple -module, then is a
strongly -regular ring. In particular, under these assumptions, is a
Cohen-Macaulay normal domain.Comment: 9 pages, to appear in Proceedings of the American Mathematical
Societ
On the existence of -thresholds and related limits
The -thresholds are important numerical invariants in prime
characteristic, whose existence had been established only under certain
assumptions. We show the existence of -thresholds in full generality. We
study properties of standard graded algebras over a field for which -pure
threshold and -threshold at the irrelevant maximal ideal agree. We also
exhibit explicit bounds for the -invariants and Castelnuovo-Mumford
regularity of Frobenius powers of ideals in terms of -thresholds and
-pure thresholds, obtaining existence of related limits in certain cases.Comment: 21 page
An algorithm for constructing certain differential operators in positive characteristic
Given a non-zero polynomial in a polynomial ring with coefficients in
a finite field of prime characteristic , we present an algorithm to compute
a differential operator which raises to its th power. For
some specific families of polynomials, we also study the level of such a
differential operator , i.e., the least integer such that
is -linear. In particular, we obtain a characterization of
supersingular elliptic curves in terms of the level of the associated
differential operator.Comment: 23 pages. Comments are welcom
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