Abstract Ring properties of amalgamated products are investigated. We offer new, elementary arguments which extend results from [5] and [12] to noncommutative setting also give new rings.

We introduce a new general construction, denoted by R 1 E, called the amalgamated duplication of a ring R along an R–module E, that we assume to be an ideal in some overring of R. (Note that, when E = 0, R1E coincides with the Nagata’s idealization R⋉E.) After discussing the main properties of the amalgamated duplication R 1E in relation with pullback–type constructions, we restrict our investi...

After recalling briefly the main properties of the amalgamated duplication of a ring R along an ideal I , denoted by R1 I [5], we restrict our attention to the study of the properties of R1 I , when I is a multiplicative canonical ideal of R [9]. In particular, we study when every regular fractional ideal of R1I is divisorial.

The Bianchi groups are a family of discrete subgroups of PSL2(C) which have group theoretic descriptions as amalgamated products and HNN extensions. Using Bass-Serre theory, we show how the cohomology of these two constructions relates to the cohomology of their pieces. We then apply these results to calculate the mod-2 cohomology ring for various Bianchi groups.

In this paper, we study the classes of rings in which every proper (regular) ideal can be factored as an invertible times a nonempty product radical ideals. More precisely, investigate stability these properties under homomorphic image and their transfer to various contexts constructions such direct product, trivial ring extension amalgamated duplication along ideal. Our results generate exampl...