-категоричные коммутативные кольца
Let be a commutative ring with nonzero identity, let be the set of all ideals of and an expansion of ideals of defined by . We introduce the concept of -primary ideals in commutative rings. A proper ideal of is called a -primary ideal if whenever and , then or . Our purpose is to extend the concept of -ideals to -primary ideals of commutative rings. Then we investigate the basic properties of -primary ideals and also discuss the relations among -primary, -primary and...
The relative cohomology of the contact Lie superalgebra with coefficients in the space of differential operators acting on tensor densities on , is calculated in N. Ben Fraj, I. Laraied, S. Omri (2013) and the generating -cocycles are expressed in terms of the infinitesimal super-Schwarzian derivative -cocycle , which is invariant with respect to the conformal subsuperalgebra of . In this work we study the supergroup case. We give an explicit construction of -cocycles of the group...
We study 2-frieze patterns generalizing that of the classical Coxeter-Conway frieze patterns. The geometric realization of this space is the space of -gons (in the projective plane and in 3-dimensional vector space) which is a close relative of the moduli space of genus curves with marked points. We show that the space of 2-frieze patterns is a cluster manifold and study its algebraic and arithmetic properties.
R. Hartshorne and A. Hirschowitz proved that a generic collection of lines on ℙn, n≥3, has bipolynomial Hilbert function. We extend this result to a specialization of the collection of generic lines, by considering a union of lines and 3-dimensional sundials (i.e., a union of schemes obtained by degenerating pairs of skew lines).
Let and be commutative rings with unity, a ring homomorphism and an ideal of . Then the subring and of is called the amalgamation of with along with respect to . In this paper, we determine when is a (generalized) filter ring.