An Upper Bound on the Reduction Number of an Ideal
نویسندگان
چکیده
Let A be a commutative ring and I an ideal of A with a reduction Q. In this paper we give an upper bound on the reduction number of I with respect to Q, when a suitable family of ideals in A is given. As a corollary it follows that if some ideal J containing I satisfies J = QJ , then I = QI, where v denotes the number of generators of J/I as an A-module.
منابع مشابه
An upper bound for the regularity of powers of edge ideals
A recent result due to Ha and Van Tuyl proved that the Castelnuovo-Mumford regularity of the quotient ring $R/I(G)$ is at most matching number of $G$, denoted by match$(G)$. In this paper, we provide a generalization of this result for powers of edge ideals. More precisely, we show that for every graph $G$ and every $sgeq 1$, $${rm reg}( R/ I(G)^{s})leq (2s-1) |E(G)|^{s-1} {rm ma...
متن کاملOn trees attaining an upper bound on the total domination number
A total dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every vertex of $G$ has a neighbor in $D$. The total domination number of a graph $G$, denoted by $gamma_t(G)$, is~the minimum cardinality of a total dominating set of $G$. Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International ournal of Graphs and Combinatorics 1 (2004), 6...
متن کاملNew results on upper domatic number of graphs
For a graph $G = (V, E)$, a partition $pi = {V_1,$ $V_2,$ $ldots,$ $V_k}$ of the vertex set $V$ is an textit{upper domatic partition} if $V_i$ dominates $V_j$ or $V_j$ dominates $V_i$ or both for every $V_i, V_j in pi$, whenever $i neq j$. The textit{upper domatic number} $D(G)$ is the maximum order of an upper domatic partition. We study the properties of upper domatic number and propose an up...
متن کاملA Study of Precision Forging of Steel Spur Gears: Upper Bound Model and Experiments
Precision forging process is widely used for the production of spur gears due to its advantages such as improved strength and surface finish, little waste of materials and reduction in the machining time of the gear. An important aspect of precision forging process is the load required to perform the process successfully and design the forging tools. In this research, a new kinematically admiss...
متن کاملAn Upper Bound on the First Zagreb Index in Trees
In this paper we give sharp upper bounds on the Zagreb indices and characterize all trees achieving equality in these bounds. Also, we give lower bound on first Zagreb coindex of trees.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008