ar X iv : m at h / 04 06 31 1 v 3 [ m at h . A C ] 2 0 Ju n 20 06 MODULE STRUCTURE OF AN INJECTIVE RESOLUTION

ar X iv : m at h / 04 06 31 1 v 1 [ m at h . A C ] 1 6 Ju n 20 04 MODULE STRUCTURE OF AN INJECTIVE RESOLUTION

Let A be the ring obtained by localizing the polynomial ring κ[X,Y, Z,W ] over a field κ at the maximal ideal (X, Y, Z,W ) and modulo the ideal (XW − Y Z). Let p be the ideal of A generated by X and Y . We study the module structure of a minimal injective resolution of A/p in details using local cohomology. Applications include the description of Ext A (M,A/p), where M is a module constructed b...

ar X iv : m at h / 06 06 31 2 v 1 [ m at h . A C ] 1 3 Ju n 20 06 ASYMPTOTIC BEHAVIOR OF MULTIGRADED REGULARITY

Let S be a standard N k-graded polynomial ring over a field K, let I be a multigraded homogeneous ideal of S, and let M be a finitely generated Z k-graded S-module. We prove that the resolution regularity, a multigraded variant of Castelnuovo-Mumford regularity, of I n M is asymptotically a linear function. This shows that the well known Z-graded phenomenon carries to multigraded situation.

ar X iv : m at h / 06 06 27 5 v 1 [ m at h . A T ] 1 2 Ju n 20 06 MODULES IN MONOIDAL MODEL CATEGORIES

This paper studies the existence of and compatibility between derived change of ring, balanced product, and function module derived functors on module categories in monoidal model categories.

ar X iv : m at h / 06 06 67 1 v 1 [ m at h . A C ] 2 7 Ju n 20 06 PRÜFER ⋆ – MULTIPLICATION DOMAINS AND ⋆ – COHERENCE

ar X iv : m at h / 01 06 13 1 v 1 [ m at h . O A ] 1 5 Ju n 20 01 INJECTIVE ENVELOPES OF C ∗ - ALGEBRAS AS OPERATOR MODULES

In this paper we give some characterizations of M. Hamana’s injective envelope I(A) of a C∗-algebra A in the setting of operator spaces and completely bounded maps. These characterizations lead to simplifications and generalizations of some known results concerning completely bounded projections onto C∗-algebras. We prove that I(A) is rigid for completely bounded A-module maps. This rigidity yi...