Let $R$ be a commutative ring with identity‎. ‎A proper ideal $P$ of $R$ is a $(n-1,n)$-$Phi_m$-prime ($(n-1,n)$-weakly prime) ideal if $a_1,ldots,a_nin R$‎, ‎$a_1cdots a_nin Pbackslash P^m$ ($a_1cdots a_nin Pbackslash {0}$) implies $a_1cdots a_{i-1}a_{i+1}cdots a_nin P$‎, ‎for some $iin{1,ldots,n}$; ($m,ngeq 2$)‎. ‎In this paper several results concerning $(n-1,n)$-$Phi_m$-prime and $(n-1,n)$-...

A neutron interferometric test of interaction-free detection of the presence of an absorbing object in one arm of a neutron interferometer has been performed. Despite deviations from the ideal performance characteristics of a Mach-Zehnder interferometer it could be shown that information is obtained without interaction.

1. Primary ideals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Primary modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3. Primary decompositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 4. More ways to get associated primes . . . . . . . . . . . . . . . . . . . . . . . 12 5. Witnesses . . . . . . . . . . . . . . . . . . ...

The purpose of this paper is to introduce and discuss the concept of T-rough (prime, primary) ideal and T-rough fuzzy (prime, primary) ideal in a commutative ring . Our main aim in this paper is, generalization of theorems which have been proved in [6, 7, 11]. At first, T-rough sets introduced by Davvaz in [6]. By using the paper, we define a concept of T-rough ideal , T-rough quotient ideal an...

In this paper, we introduce the notions of expansion of ideals in $MV$-algebras, $ (tau,sigma)- $primary, $ (tau,sigma)$-obstinate  and $ (tau,sigma)$-Boolean  in $ MV- $algebras. We investigate the relations of them. For example, we show that every $ (tau,sigma)$-obstinate ideal of an $ MV-$ algebra is $ (tau,sigma)$-primary  and $ (tau,sigma)$-Boolean. In particular, we define an expansion $ ...

this paper is devoted to the study of determining optimal process mean in system production with the two markets for the sale of goods. in this paper, we developed an absorbing markov chain model in production systems where all items are inspected %100 for conformance with their specification limits. when the value of the quality characteristic of an item falls below a lower limit, the item is ...