semistar dimension of polynomial rings and prufer-like domains
نویسندگان
چکیده
let $d$ be an integral domain and $star$ a semistar operation stable and of finite type on it. we define the semistar dimension (inequality) formula and discover their relations with $star$-universally catenarian domains and $star$-stably strong s-domains. as an application, we give new characterizations of $star$-quasi-pr"{u}fer domains and um$t$ domains in terms of dimension inequality formula (and the notions of universally catenarian domain, stably strong s-domain, strong s-domain, and jaffard domain). we also extend arnold's formula to the setting of semistar operations.
منابع مشابه
Semistar dimension of polynomial rings and Prufer-like domains
Let $D$ be an integral domain and $star$ a semistar operation stable and of finite type on it. We define the semistar dimension (inequality) formula and discover their relations with $star$-universally catenarian domains and $star$-stably strong S-domains. As an application, we give new characterizations of $star$-quasi-Pr"{u}fer domains and UM$t$ domains in terms of dimension inequal...
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عنوان ژورنال:
bulletin of the iranian mathematical societyناشر: iranian mathematical society (ims)
ISSN 1017-060X
دوره 37
شماره No. 3 2011
میزبانی شده توسط پلتفرم ابری doprax.com
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