In the last twenty years several methods for computing primary decompositions of ideals in multivariate polynomial rings over fields (Seidenberg (1974), Lazard (1985), Kredel (1987), Eisenbud et al. (1992)), the integers (Seidenberg, 1978), factorially closed principal ideal domains (Ayoub (1982), Gianni et al. (1988)) and more general rings (Seidenberg, 1984) have been proposed. A related prob...

we state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. in particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. also we show that if m is an strong comultiplicati...

The debts’ clearing problem is about clearing all the debts in a group of n entities (eg. persons, companies) using a minimal number of money transaction operations. In a previous paper we conjectured the problem to be NP-complete. In this paper we prove that it is NP-hard in the strong sense and also NP-easy. We also show the same results for a restricted version of the problem.

Based on prime factorisation in number theory, a new but simple and efficient protection method for access control is proposed. This method has several advantages on performance over previous methods in the literature. Especially, a file I user can be added to or removed from the system without much effort. Excellence of this method is more pronounced for those systems where files are accessibl...

We investigate the instability of the Cauchy horizon caused by causality violation in the compact vacuum universe with the topology B × S × R, which Moncrief and Isenberg considered. We show that if the occurrence of curvature singularities are restricted to the boundary of causality violating region, the whole segments of the boundary become curvature singularities. This implies that the stron...