In this paper we use "ring changed'' Gorenstein homologicaldimensions to define Cohen-Macaulay injective, projective and flatdimensions. For doing this we use the amalgamated duplication of thebase ring with semi-dualizing ideals. Among other results, we prove that finiteness of these new dimensions characterizes Cohen-Macaulay rings with dualizing ideals.

‎We say that a module $M$ is a emph{cms-module} if‎, ‎for every cofinite submodule $N$ of $M$‎, ‎there exist submodules $K$ and $K^{'}$ of $M$ such that $K$ is a supplement of $N$‎, ‎and $K$‎, ‎$K^{'}$ are mutual supplements in $M$‎. ‎In this article‎, ‎the various properties of cms-modules are given as a generalization of $oplus$-cofinitely supplemented modules‎. ‎In particular‎, ‎we prove tha...

In this paper, we introduce the “semi-topological K-homology” of complex varieties, a theory related to semi-topological K-theory much as connective topological K-homology is related to connective topological K-theory. Our main theorem is that the semi-topological K-homology of a smooth, quasiprojective complex variety Y coincides with the connective topological Khomology of the associated anal...

‎we say that a module $m$ is a emph{cms-module} if‎, ‎for every cofinite submodule $n$ of $m$‎, ‎there exist submodules $k$ and $k^{'}$ of $m$ such that $k$ is a supplement of $n$‎, ‎and $k$‎, ‎$k^{'}$ are mutual supplements in $m$‎. ‎in this article‎, ‎the various properties of cms-modules are given as a generalization of $oplus$-cofinitely supplemented modules‎. ‎in particular‎, ‎we prove tha...

In this paper we study isotropic Lagrangian submanifolds , in complex space forms . It is shown that they are either totally geodesic or minimal in the complex projective space , if . When , they are either totally geodesic or minimal in . We also give a classification of semi-parallel Lagrangian H-umbilical submanifolds.

In a perfect category every object has a minimal projective resolution. We give a sufficient condition for the category of modules over a category-graded algebra to be perfect. AMS Subject Classification (2000): 18E15, 16W50. In [6] the second author explored homological properties of algebras graded over a small category. Our interest in these algebras arose from our research on the homologica...

Using limit linear series and a result controlling degeneration from separable maps to inseparable maps, we give a formula for the number of rational functions (up to automorphism of the target) on the projective line with ramification to order ei at general points Pi, in the case that all ei are less than the characteristic. Unlike the case of characteristic 0, the answer is not given by Schub...