N. Mahdou

Department of Mathematics, Faculty of Science and Technology of Fez, Box 2202, University S.M. Ben Abdellah Fez, Morocco

[ 1 ] - Coherence in amalgamated algebra along an ideal

Let $f: Arightarrow B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we investigate the transfer of the property of coherence to the amalgamation $Abowtie^{f}J$. We provide necessary and sufficient conditions for $Abowtie^{f}J$ to be a coherent ring.

[ 2 ] - When every $P$-flat ideal is flat

In this paper‎, ‎we study the class of rings in which every $P$-flat‎ ‎ideal is flat and which will be called $PFF$-rings‎. ‎In particular‎, ‎Von Neumann regular rings‎, ‎hereditary rings‎, ‎semi-hereditary ring‎, ‎PID and arithmetical rings are examples of $PFF$-rings‎. ‎In the context domain‎, ‎this notion coincide with‎ ‎Pr"{u}fer domain‎. ‎We provide necessary and sufficient conditions for‎...

[ 3 ] - Some homological properties of amalgamated duplication of a ring along an ideal

In this work, we investigate the transfer of some homological properties from a ring $R$ to its amalgamated duplication along some ideal $I$ of $R$ $Rbowtie I$, and then generate new and original families of rings with these properties.