2 In the hallway of the university Wittgenstein asked a colleague: " I've always wondered why for so long people thought that the sun revolved around the earth. " " Why? " said his surprised interlocutor, " well, I suppose it just looks that way. " " Hmm " , retorted Wittgenstein, " and what would it look like if the earth revolved around the sun? " This puzzled the interlocutor.

in this paper, we study some ring theoretic properties of the amalgamated duplication ring $rbowtie i$ of a commutative noetherian ring $r$ along an ideal $i$ of $r$ which was introduced by d'anna and fontana. indeed, it is determined that when $rbowtie i$ satisfies serre's conditions $(r_n)$ and $(s_n)$, and when is a normal ring, a generalized cohen-macaulay ring and finally a filter ring.

The design issues for group mutual exclusion have been modeled by Joung as the Congenial Talking Philosophers, and solutions for shared-memory models and complete message-passing networks have been proposed [2, 3]. These solutions, however, cannot be straightforwardly and efficiently converted to ring networks where each philosopher can only communicate directly with its two neighboring philoso...