We obtain a complete structural characterization of Cohn-Leavitt algebras over no-exit objects as graded involutive algebras. Corollaries of this result include graph-theoretic conditions characterizing when a Leavitt path algebra is a directed union of (graded) matricial algebras over the underlying field and over the algebra of Laurent polynomials and when the monoid of isomorphism classes of...

for making many comments and corrections concerning these notes. All rings are commutative and contain multiplicative identity, moreover we will always insist that ring homomorphisms respect the multiplicative identity element. Local rings are assumed to be Noetherian. Additionally, all modules are unitary modules. We have made an attempt to be consistent with our notation: (1) Rings are often ...

We study classes of modules over a commutative ring which allow to do homological algebra relative to such a class. We classify those classes consisting of injective modules by certain subsets of ideals. When the ring is Noetherian the subsets are precisely the generization closed subsets of the spectrum of the ring.

We classify all the localizing subcategories of the derived category D(R) of modules over a noetherian ring R, after developing the theory of unbounded complexes over R. Then, we use this classification to classify thick subcategories of the derived category D(R)proj of bounded complexes of projective modules over R, and prove Balmer’s reconstruction theorem in the affine case.

This paper generalize the idea of the authors in J. Pure Appl. Algebra 210 (2007) 437–445. Namely, we define and study a particular case of Gorenstein projective modules. We investigate some change of rings results for this new kind of modules. Examples over not necessarily Noetherian rings are given.

A module is called uniseriat if it has a unique composition series of finite length. A ring (always with 1) is called serial if its right and left free modules are direct sums of uniserial modules. Nakayama, who called these rings generalized uniserial rings, proved [21, Theorem 171 that every finitely generated module over a serial ring is a direct sum of uniserial modules. In section one we g...

Let $(R,underline{m})$ be a commutative Noetherian local ring and $M$ be a non-zero finitely generated $R$-module. We show that if $R$ is almost Cohen-Macaulay and $M$ is perfect with finite projective dimension, then $M$ is an almost Cohen-Macaulay module. Also, we give some necessary and sufficient condition on $M$ to be an almost Cohen-Macaulay module, by using $Ext$ functors.