The notion of quasi-exact sequence of modules was introduced by B. Davvaz and coauthors in 1999 as a generalization of the notion of exact sequence. In this paper we investigate further this notion. In particular, some interesting results concerning this concept and torsion functor are given.

The isomorphism problem for finitely generated Coxeter groups is the problem of deciding if two finite Coxeter matrices define isomorphic Coxeter groups. Coxeter [3] solved this problem for finite irreducible Coxeter groups. Recently there has been considerable interest and activity on the isomorphism problem for arbitrary finitely generated Coxeter groups. For a recent survey, see Mühlherr [10...

One of the most important property of the computability is the certainty. For example a set of natural numbers is computable if there is a Turing machine which decides certainly if a given natural number belongs to the set or not, and no wrong answers are tolerant. On the other hand, the finitely bounded computability discussed in this paper allows finitely many mistakes which can be eventually...

We prove the following theorem for a finitely generated field K: Let M be a Galois extension of K which is not separably closed. Then M is not PAC over K.

We study infinite but finitely representable databases based on constraints, motivated by new database applications such as those involving spatio-temporal information. We introduce a general definition of finite representation, and define the concept of a query as a generalization of a query over relational databases. We investigate the theory of finitely representable models and prove that it...

But before starting on this, let me try to explain again, in a different way, our approach. The one habit I’ve been trying to wean you of is the an over-reliance upon concrete examples to develop your understanding. The vector space R is a very concrete and familar example of a vector space over a field. To do calculations in this setting all you need to do is apply arithmetic (over and over an...

We show that the subconstruct Fing of Prtop, consisting of all finitely generated pretopological spaces, is the largest Cartesian closed coreflective subeonstmct of Prtop. This implies that in any coreflective subconstruct of Prtop, exponential objects are finitely generated. Moreover, in any finitely productive, coreflective subconstruct, exponential objects are precisely those objects of the ...