UMT-Domain Property in Pullbacks of Graded Integral Domains

UMT-Domain Property in Pullbacks of Graded Integral Domains Let $$\Gamma$$ Γ be a torsionless commutative cancellative monoid, $$T=\bigoplus _{\alpha \in \Gamma }T_{\alpha }$$ T = ⨁ α ∈ Γ T α be a $$\Gamma$$ Γ -graded integral domain, $$M = \bigoplus _{\alpha \in \Gamma }M_{\alpha }$$ M = ⨁ α ∈ Γ M α be a maximal homogeneous ideal of T, $$k=T/M$$ k = T / M (so $$k = \bigoplus _{\alpha \in \Gamma }T_{\alpha }/M_{\alpha }$$ k = ⨁ α ∈ Γ T α / M α ), $$\varphi :T\rightarrow k$$ φ : T → k be the canonical surjection, D be a $$\Gamma$$ Γ -graded subring of k, F be the homogeneous quotient field of D, and $$R= \varphi ^{-1}(D)$$ R = φ - 1 ( D ) . In this paper, among other things, we show that R is a UMT-domain (resp., PvMD, graded-Prüfer domain) if and only if T and D are UMT-domains (resp., PvMDs, graded-Prüfer domains), M is a maximal t-ideal of T, and k is algebraic over F (resp., $$k=F$$ k = F ). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Iranian Mathematical Society Springer Journals

UMT-Domain Property in Pullbacks of Graded Integral Domains

, Volume 44 (3) – Jun 4, 2018
19 pages

Publisher
Springer Journals
Subject
Mathematics; Mathematics, general
ISSN
1017-060X
eISSN
1735-8515
D.O.I.
10.1007/s41980-018-0040-y
Publisher site
See Article on Publisher Site

Abstract

Let $$\Gamma$$ Γ be a torsionless commutative cancellative monoid, $$T=\bigoplus _{\alpha \in \Gamma }T_{\alpha }$$ T = ⨁ α ∈ Γ T α be a $$\Gamma$$ Γ -graded integral domain, $$M = \bigoplus _{\alpha \in \Gamma }M_{\alpha }$$ M = ⨁ α ∈ Γ M α be a maximal homogeneous ideal of T, $$k=T/M$$ k = T / M (so $$k = \bigoplus _{\alpha \in \Gamma }T_{\alpha }/M_{\alpha }$$ k = ⨁ α ∈ Γ T α / M α ), $$\varphi :T\rightarrow k$$ φ : T → k be the canonical surjection, D be a $$\Gamma$$ Γ -graded subring of k, F be the homogeneous quotient field of D, and $$R= \varphi ^{-1}(D)$$ R = φ - 1 ( D ) . In this paper, among other things, we show that R is a UMT-domain (resp., PvMD, graded-Prüfer domain) if and only if T and D are UMT-domains (resp., PvMDs, graded-Prüfer domains), M is a maximal t-ideal of T, and k is algebraic over F (resp., $$k=F$$ k = F ).

Journal

Bulletin of the Iranian Mathematical SocietySpringer Journals

Published: Jun 4, 2018

DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month Explore the DeepDyve Library Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve Freelancer DeepDyve Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations