On finitely generated projective modules

It is shown that the set End _A (M) is a Waelbroeck algebra, for every topological Waelbroeck algebraA and for every finitely generated projectiveA-moduleM. The research of Mart Abel was supported by Greek State Scholarship Foundation and Estonian Science Foundation grant 6205.     

On finitely generated projective modules and multiplication modules

This paper is based on the M. Sc. thesis written by the third author under the supervision of the first two authors. It was submitted to the University of Baghdad in January 1987.     

On projective modules over quantum polynomials

The present paper can be considered as a continuation of [6] and includes an extension of the main result of [1]. This research is partially supported by the Russian Foundation for Basic Research and by INTAS, grant No. 93-2618. Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 40, Algebra-6, 1996.     

On supplementation and generalized projective modules

Discrete (quasi) modules form an important class in module theory, they are studied extensively by many authors. The decomposition theorem for quasidiscrete modules plays an important rule in the better understanding of such modules. In fact, every quasidiscrete module is a direct sum of hollow submodules. Here we introduce some new concepts (weak quasidiscrete, and S ₁- and S ₂-supplemented modules) which generalize the concept of quasidiscrete module. We show that some of the properties of quasidiscrete modules still hold in the class of weak quasidiscrete modules. We also obtain some properties of weak quasidiscrete modules, which are similar to the properties known for quasidiscrete modules. We introduce the concept of generalized relative projectivity (relative S-projectivemodules), and use it to characterize direct sums of hollowmodules. In fact, relative S-projectivity is an essential condition for direct sums of hollow modules to be weak quasidiscrete modules.     

On loewy lengths of projective modules for p-solvable groups

We give an example of the nonregular ring every one-sided ideal of which is generated by idempotents, It is also proved that if each right ideal of a ring R is generated by idempotents and each primitive factor ring of a ring R has a bounded index of nilpotency then R is regular.     

Patching theorems for projective modules

In the first section of this paper, we prove several ‘Milnor-Mayer-Vietoris’-type patching theorems for projective modules. In the second section we apply these theorems to projective modules over polynomial rings and give some criteria for such modules to be extended. In the third section, the theorems are applied to the study of vector bundles over curves.