Universally catenarian domains of D+M type, II
Let T be a domain of the form K+M, where K is a field and M is a maximal ideal of T. Let D be a subring of K such that R=D+M is universally catenarian. Then D is universally catenarian and K is algebraic over k, the quotient field of D. If [K:k]<∞, then T is universally catenarian. Consequently,...
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| Format: | Article |
| Language: | English |
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Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171291000212 |
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| _version_ | 1832554732191744000 |
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| author | David E. Dobbs Marco Fontana |
| author_facet | David E. Dobbs Marco Fontana |
| author_sort | David E. Dobbs |
| collection | DOAJ |
| description | Let T be a domain of the form K+M, where K is a field and M is a maximal ideal
of T. Let D be a subring of K such that R=D+M is universally catenarian. Then D is
universally catenarian and K is algebraic over k, the quotient field of D. If [K:k]<∞, then T is
universally catenarian. Consequently, T is universally catenarian if R is either Noetherian or a
going-down domain. A key tool establishes that universally going-between holds for any domain
which is module-finite over a universally catenarian domain. |
| format | Article |
| id | doaj-art-c3e3e02af11944d0805eff815d5808e1 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c3e3e02af11944d0805eff815d5808e12025-02-03T05:50:47ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-0114220921410.1155/S0161171291000212Universally catenarian domains of D+M type, IIDavid E. Dobbs0Marco Fontana1Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, USADipartimento di Matematica, Universita di Roma, “La Sapienza”, Roma 00185, ItalyLet T be a domain of the form K+M, where K is a field and M is a maximal ideal of T. Let D be a subring of K such that R=D+M is universally catenarian. Then D is universally catenarian and K is algebraic over k, the quotient field of D. If [K:k]<∞, then T is universally catenarian. Consequently, T is universally catenarian if R is either Noetherian or a going-down domain. A key tool establishes that universally going-between holds for any domain which is module-finite over a universally catenarian domain.http://dx.doi.org/10.1155/S0161171291000212universally catenariangoing betweenaltitude formula. |
| spellingShingle | David E. Dobbs Marco Fontana Universally catenarian domains of D+M type, II International Journal of Mathematics and Mathematical Sciences universally catenarian going between altitude formula. |
| title | Universally catenarian domains of D+M type, II |
| title_full | Universally catenarian domains of D+M type, II |
| title_fullStr | Universally catenarian domains of D+M type, II |
| title_full_unstemmed | Universally catenarian domains of D+M type, II |
| title_short | Universally catenarian domains of D+M type, II |
| title_sort | universally catenarian domains of d m type ii |
| topic | universally catenarian going between altitude formula. |
| url | http://dx.doi.org/10.1155/S0161171291000212 |
| work_keys_str_mv | AT davidedobbs universallycatenariandomainsofdmtypeii AT marcofontana universallycatenariandomainsofdmtypeii |