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Topics on symbolic Rees algebras for space monomial curves
| Content Provider | Scilit |
|---|---|
| Author | Goto, Shiro Nishida, Koji Shimoda, Yasuhiro |
| Copyright Year | 1991 |
| Description | Let A be a regular local ring of dim A = 3 and p a prime ideal in A of dim A/p = 1. We put $R_{s}$(p) = (here t denotes an indeterminate over A) and call it the symbolic Rees algebra of p. With this notation the authors [5, 6] investigated the condition under which the A-algebra $R_{s}$(p) is Cohen-Macaulay and gave a criterion for $R_{s}$(p) to be a Gorenstein ring in terms of the elements f and g in Huneke’s condition [11, Theorem 3.1] of $R_{s}$(p) being Noetherian. They furthermore explored the prime ideals p = $p(n_{1}$, $n_{2}$, $n_{3}$) in the formal power series ring A = k[X, Y, Z] over a field k defining space monomial curves and Z = with $GCD(n_{1}$, $n_{2}$, $n_{z}$) = 1 and proved that $R_{s}$(p) are Gorenstein rings for certain prime ideals p = $p(n_{1}$ $n_{2}$, $n_{3}$). In the present research, similarly as in [5, 6], we are interested in the ring-theoretic properties of $R_{s}$(p) mainly for p = $p(n_{1}$ $n_{2)}$ $n_{z}$) and the results of [5, 6] will play key roles in this paper. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/64029E9EC6FD0675A309F2B161A22359/S0027763000003792a.pdf/div-class-title-topics-on-symbolic-rees-algebras-for-space-monomial-curves-div.pdf |
| ISSN | 00277630 |
| e-ISSN | 21526842 |
| DOI | 10.1017/s0027763000003792 |
| Journal | Nagoya Mathematical Journal |
| Volume Number | 124 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1991-12-01 |
| Access Restriction | Open |
| Subject Keyword | Nagoya Mathematical Journal Space Monomial Monomial Curves Prime Ideals N1 N2 |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
