The purpose of this paper is to review the current state of some key questions of the area
indicated in the title. Recently, in Romania and elsewhere, some mathematicians began to …

" Topological homology" is a short title for the homological theme in the theory of Banach
and polynormed algebras. It is of comparatively recent usage, in Romania and somewhere …

In the study of modules the theory of submodules is the analogue of the ideal theory of a
Banach algebra. We will develop some theory for closed maximal submodules and prove …

We develop higher dimensional amenability for Banach algebras from the viewpoint of
Banach homology theory. In particular, we show that such amenability is equivalent to the …

As is known, in pure algebra each module M over an algebra A possesses projective and
injective resolvents [2, 3]. Unfortunately, the corresponding assertion is not proved in its full …

Linear maps on Banach A-modules X are considered, and in the particular case of a
bounded module map'from X into the Banach algebra A, it is mainly shown that X bears a …

In this paper, we investigate homological properties of Banach algebras. We show that
retractions Banach algebras preserve biprojectivity, contractibility and biflatness. We also …

For a large class of Banach algebras we solve the Cohomology Comparison Problem for the
second cohomology groups, in that we prove that for all amenable strongly regular Banach …

A characterisation of closed subalgebras of Page 1 Proceedings of the Edinburgh Mathematical
Society (1976-77), 20, 215-217 © A CHARACTERISATION OF CLOSED SUB ALGEBRAS OF …

1. Introduction. Let B and B1 be two (real or complex) Banach algebras. A number of known
results [3],[6],[12],[13] give conditions on the algebras under which certain classes of …