منابع مشابه
On generalisations of almost prime and weakly prime ideals
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 $(n-1,n)$-...
متن کاملon generalisations of almost prime and weakly prime ideals
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 $(n-1,n)$-...
متن کاملCongruences for Overpartition K-tuples
An overpartition of the nonnegative integer n is a non-increasing sequence of natural numbers whose sum is n in which the first occurrence of a number may be overlined. Let k ≥ 1 be an integer. An overpartition k-tuple of a positive integer n is a k-tuple of overpartitions wherein all listed parts sum to n. Let pk(n) be the number of overpartition k-tuples of n. In this paper, we will give a sh...
متن کاملSome Arithmetic Properties of Overpartition K -tuples
Abstract Recently, Lovejoy introduced the construct of overpartition pairs which are a natural generalization of overpartitions. Here we generalize that idea to overpartition ktuples and prove several congruences related to them. We denote the number of overpartition k-tuples of a positive integer n by pk(n) and prove, for example, that for all n ≥ 0, pt−1(tn + r) ≡ 0 (mod t) where t is prime a...
متن کاملComputing Critical $k$-tuples in Power Networks
In this paper the problem of finding the sparsest (i.e., minimum cardinality) critical k-tuple including one arbitrarily specified measurement is considered. The solution to this problem can be used to identify weak points in the measurement set, or aid the placement of new meters. The critical k-tuple problem is a combinatorial generalization of the critical measurement calculation problem. Us...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2006
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2005.11.014