| Title:
|
The general structure of inverse polynomial modules (English) |
| Author:
|
Park, Sangwon |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
343-349 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we compute injective, projective and flat dimensions of inverse polynomial modules as $R[x]$-modules. We also generalize Hom and Ext functors of inverse polynomial modules to any submonoid but we show Tor functor of inverse polynomial modules can be generalized only for a symmetric submonoid. (English) |
| Keyword:
|
module |
| Keyword:
|
inverse polynomial |
| Keyword:
|
homological dimensions |
| Keyword:
|
Hom |
| Keyword:
|
Ext |
| Keyword:
|
Tor |
| MSC:
|
13C11 |
| MSC:
|
16D50 |
| MSC:
|
16D80 |
| MSC:
|
16E05 |
| MSC:
|
16E10 |
| MSC:
|
16E30 |
| MSC:
|
16S36 |
| idZBL:
|
Zbl 0983.16006 |
| idMR:
|
MR1844314 |
| . |
| Date available:
|
2009-09-24T10:42:54Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127651 |
| . |
| Reference:
|
[1] F. S. Macaulay: The algebraic theory of modular system.Cambridge Tracts in Math. 19 (1916). |
| Reference:
|
[2] H. Matsumura: Commutative Algebra.W. A. Benjamin, Inc., New York, 1970. Zbl 0211.06501, MR 0266911 |
| Reference:
|
[3] A. S. McKerrow: On the injective dimension of modules of power series.Quart J. Math. Oxford Ser. (2), 25 (1974), 359–368. Zbl 0302.16027, MR 0371881, 10.1093/qmath/25.1.359 |
| Reference:
|
[4] D. G. Northcott: Injective envelopes and inverse polynomials.J. London Math. Soc. (2), 8 (1974), 290–296. Zbl 0284.13012, MR 0360555 |
| Reference:
|
[5] S. Park: Inverse polynomials and injective covers.Comm. Algebra 21 (1993), 4599–4613. Zbl 0794.16004, MR 1242851, 10.1080/00927879308824819 |
| Reference:
|
[6] S. Park: The Macaulay-Northcott functor.Arch. Math. (Basel) 63 (1994), 225–230. Zbl 0804.18009, MR 1287251, 10.1007/BF01189824 |
| Reference:
|
[7] J. Rotman: An Introduction to Homological Algebra.Academic Press Inc., New York, 1979. Zbl 0441.18018, MR 0538169 |
| . |
