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The Theory of pre-Krull Domains

Author: LiQing
Tutor: WangFangGui
School: Sichuan Normal University
Course: Basic mathematics
Keywords: v- ideal Tolerancing w- dimensional pre-Krull ring of integers UMT - Polynomial ring
CLC: O153.3
Type: Master's thesis
Year: 2005
Downloads: 24
Quote: 0
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Abstract


In this paper, the use of the star operator to characterize the entire pre-Krull ring . First, we discuss the pre-Krull ring with several major categories throughout the whole relationship between the rings . Proved that R is a finite local principal ideal characteristics and satisfying ascending chain condition pre-Krull entire ring if and only if R is a Krull whole ring . And gives the whole ring R if each ring expansion is pre-Krull ring of integers and not a domain , then R is a generalized Dedekind ring is Prüfer whole entire ring . As well as in pre-Krull whole polynomial ring on the ring of fractions is still pre-Krull ring ring of integers conditions , pre-Krull ring of integers of each t-linked ring expansion is still pro-Krull entire ring . Also proved that pre-Krull ring of integers in prime v- ideal localization is followed by discrete valuation ring . ring . Secondly, the whole discussion of the pre-Krull ring and ring UMT whole polynomial ring and w- dimensional relations . Proved that R is a pre-Krull ring if and only if the entire R [{X α }] is pre-Krull ring if and only if the entire R [{X α ) ] N v is a generalized Dedekind ring of integers if and only if R [{X α }] N v is a pseudo- principal ideal .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Abstract algebra ( Algebra ) > Ring Theory
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