Radical of splitting ring extensions.
Radical properties of perfect modules.
Radicals of symmetric cellular algebras
For a symmetric cellular algebra, we study properties of the dual basis of a cellular basis first. Then a nilpotent ideal is constructed. The ideal connects the radicals of cell modules with the radical of the algebra. It also yields some information on the dimensions of simple modules. As a by-product, we obtain some equivalent conditions for a finite-dimensional symmetric cellular algebra to be semisimple.
Rad-supplemented modules
Recent advances in enveloping algebras of semi-simple Lie-algebras
Recent progress in special Colombeau algebras: geometry, topology, and algebra
Over the past few years there has been considerable progress in the structural understanding of special Colombeau algebras. We present some of the main trends in this development: non-smooth differential geometry, locally convex theory of modules over the ring of generalized numbers, and algebraic aspects of Colombeau theory. Some open problems are given and directions of further research are outlined.
Reduced near-rings
Reduced p.p.-rings without identity.
Réduction des intersections.
Reduction Theorems for Endomorphism Near-Rings.
Regular additively inverse semirings.
Regular and normal quantales
Regular Rings and Baer Rings.
Relative coherence and preenvelopes.
Relative exact covers
Recently Rim and Teply [11] found a necessary condition for the existence of -torsionfree covers with respect to a given hereditary torsion theory for the category -mod. This condition uses the class of -exact modules; i.e. the -torsionfree modules for which every its -torsionfree homomorphic image is -injective. In this note we shall show that the existence of -torsionfree covers implies the existence of -exact covers, and we shall investigate some sufficient conditions for the converse....
Relative hermitian Morita theory. Part II: Hermitian Morita contexts.
We introduce the notion of a relative hermitian Morita context between torsion triples and we show how these induce equivalences between suitable quotient categories of left and right modules.Due to the lack of involutive bimodules, the induced Morita equivalences are not necessarily hermitian, however.
Relative injectivity and CS-modules.
Relative natural classes and relative injectivity.
Relative purity over Noetherian rings
Relative theory in subcategories
We generalize the relative (co)tilting theory of Auslander-Solberg in the category mod Λ of finitely generated left modules over an artin algebra Λ to certain subcategories of mod Λ. We then use the theory (relative (co)tilting theory in subcategories) to generalize one of the main result of Marcos et al. [Comm. Algebra 33 (2005)].