{"id":2399,"date":"2024-11-02T21:22:13","date_gmt":"2024-11-02T21:22:13","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=2399"},"modified":"2024-11-08T08:15:11","modified_gmt":"2024-11-08T08:15:11","slug":"a-treed-domain-need-not-be-valtreed","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/a-treed-domain-need-not-be-valtreed\/","title":{"rendered":"A treed domain need not be valtreed"},"content":{"rendered":"\n
<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n\n
\n

Moroccan Journal of Algebra and Geometry with Applications<\/strong><\/p>\n\n\n\n

Latest articles<\/a><\/p>\n<\/div>\n\n\n\n

\n
<\/div>\n<\/div>\n\n\n\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n
\n
\n

A treed domain need not be valtreed<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

David E. Dobbs <\/strong><\/i>
Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1320<\/p>\n\n\n\n

<\/div>\n\n\n\n

Pages 265-278 | Received 09 January 2024, Accepted 17 February 2024, Published 08 November 2024 <\/span><\/p>\n\n\n\n

<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n

Abstract<\/span><\/strong><\/p>\n\n\n\n

If 3 \\leq n \\leq \\infty<\/span>, there exists a quasi-local treed domain which has Krull dimension n<\/span> and is not a valtreed domain. A consequence is that the class of valtreed domains fits properly between the class of treed domains and the class of going-down domains. Although the class of treed domains that are not going-down domains is stable under the classical D+M<\/span> construction, the class of valtreed domains that are not going-down domains is markedly unstable under that construction.<\/p>\n\n\n\n

<\/p>\n\n\n\n

Keywords<\/strong>:<\/span>  Commutative ring, integral domain, prime ideal, treed domain, valuation domain, maximal ideal, valtreed domain, going-down domain, field extension, integral closure, left topology, D+M<\/span> construction.<\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> Primary 13B21, 13G05; Secondary 13A15, 13F05, 54A10.<\/p>\n\n\n\n

Downloads:<\/strong> Full-text PDF<\/a><\/p>\n<\/div>\n\n\n\n

<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
MJAGA_Volume-3_Issue-2-265-278<\/a><\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n
<\/div>\n\n\n\n
\n
\n
\n
Previous article <\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n
\n
\n
View<\/strong> issue table of contents<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n
\n
\n
Next<\/strong> article<\/a><\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Moroccan Journal of Algebra and Geometry with Applications Latest articles A treed domain need not be valtreed David E. Dobbs Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1320 Pages 265-278 | Received 09 January 2024, Accepted 17 February 2024, Published 08 November 2024 Abstract If , there exists a quasi-local treed domain which has Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-page-builder.php","meta":{"footnotes":""},"class_list":["post-2399","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2399","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/comments?post=2399"}],"version-history":[{"count":8,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2399\/revisions"}],"predecessor-version":[{"id":2509,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2399\/revisions\/2509"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=2399"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}