Local Chern classes, multiplicities, and perfect complexes
Loewy coincident algebra and -3 associated graded algebra
We prove that an associated graded algebra of a finite dimensional algebra is (= selfinjective) if and only if is and Loewy coincident. Here is said to be Loewy coincident if, for every primitive idempotent , the upper Loewy series and the lower Loewy series of and coincide. -3 algebras are an important generalization of algebras; note that Auslander algebras form a special class of these algebras. We prove that for a Loewy coincident algebra , the associated graded algebra...
Multi-graded extended Rees algebras of -primary ideals.
Multiplicities and Rees valuations.
On -Kasch spaces
If is a Tychonoff space, its ring of real-valued continuous functions. In this paper, we study non-essential ideals in . Let be a infinite cardinal, then is called -Kasch (resp. -Kasch) space if given any ideal (resp. -ideal) with then is a non-essential ideal. We show that is an -Kasch space if and only if is an almost -space and is an -Kasch space if and only if is a pseudocompact and almost -space. Let denote the socle of . For a topological space with only...
On almost discrete space
Let be the ring of real continuous functions on a completely regular Hausdorff space. In this paper an almost discrete space is determined by the algebraic structure of . The intersection of essential weak ideal in is also studied.
On associated and attached prime ideals of certain modules
Primary and secondary functors have been introduced in [2] and applied to extend some results concerning asymptotic prime ideals. In this paper, the theory of primary and secondary functors is developed and examples of non-exact primary and non-exact secondary functors are presented. Also, as an application, the sets of associated and of attached prime ideals of certain modules are determined.
On equimultiple ideals.
On -sequences associated to filtrations
On multi-Rees algebras. With an Appenddix by Ngô Viêt Trung.
On the Chern Number of a Filtration
On the Cohen-Macaulay and Gorenstein properties of multigrad rees algebras.
On the Cohen-Macaulay property of diagonal subalgebras of the Rees algebra.
On the Cohen-Macaulayness of the associated graded ring of certain monomial curves.
On the computation of symbolic powers of some curves in .
On the equations of Rees algebras.
On the Gorenstein property of form rings.
On the Gorenstein property of the associated graded Ring of a power of an ideal.
On the Gorenstein property of the diagonals of the Rees algebra.
On the Graded Algebra relative to a valuation.