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.

In this paper we construct a free resolution for a free partially commutative monoid and with its help prove the Husainov’s Conjecture. We follow the ideas of D. Cohen who built in [3] a resolution for the so-called graph product of groups, given resolutions for factors. The presentation of the graph product with the help of direct and free amalgamated products played the leading role at that. ...

When studying Haken 3-manifolds, one is led naturally to the following construction: the amalgamation of two 3-manifolds M and M ′ via a homeomorphism between their boundaries. In this paper, we study the behaviour of Heegaard genus under this operation. We show that, provided the gluing homeomorphism is ‘sufficiently complicated’ and M and M ′ satisfy some standard conditions, then the Heegaar...

The problem of integrating knowledge from multiple and heterogeneous sources is a fundamental issue in current information systems. In order to cope with this problem, the concept of mediator has been introduced as a software component providing intermediate services, linking data resources and application programs, and making transparent the heterogeneity of the underlying systems. In designin...

In this paper, first we define the notion of involutive operator on bounded involutive equality algebras and by using it, we introduce a new class of equality algebras that we called it a tense like equality algebra. Then we investigate some properties of tense like equality algebra. For two involutive bounded equality algebras and an equality homomorphism between them, we prove that the tense ...

We show that the real Cremona group of plane is a non-trivial amalgam two groups amalgamated along their intersection and give an alternative proof its abelianisation.

in this paper we characterize hyper mv -algebras in which 0 or1 are scalar elements . we prove that any nite hyper mv -algebra that 0is a scaler element in it, is an mv -algebra. finally we characterize hypermv -algebras of order 2 and order 3.

Introduction. Voiculescu’s theory of freeness in noncommutative probability spaces (see [10,11,12,13,14,15], especially the latter for an overview) has made possible the recent surge of results about and related to the free group factors L(Fn) [13,3,7,8,9,4]. One hopes to eventually be able to solve the old isomorphism question, first raised by R.V. Kadison in the 1960’s, of whether L(Fn) ∼= L(...