×
Park, Sangwon

The general structure of inverse polynomial modules. (English) Zbl 0983.16006

Czech. Math. J. 51, No. 2, 343-349 (2001).
Summary: 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 that Tor functor of inverse polynomial modules can be generalized only for a symmetric submonoid.

Cited in 3 Documents

MSC:

16E30 Homological functors on modules (Tor, Ext, etc.) in associative algebras
16E10 Homological dimension in associative algebras
16D50 Injective modules, self-injective associative rings
16S36 Ordinary and skew polynomial rings and semigroup rings

Keywords:

injective dimension; inverse polynomial modules; homological dimensions; Hom; Ext; Tor; flat dimension; projective dimension
PDFBibTeX XMLCite
\textit{S. Park}, Czech. Math. J. 51, No. 2, 343--349 (2001; Zbl 0983.16006)
Full Text: DOI EuDML

References:

[1] F. S. Macaulay: The algebraic theory of modular system. Cambridge Tracts in Math. 19 (1916). · JFM 46.0167.01
[2] H. Matsumura: Commutative Algebra. W. A. Benjamin, Inc., New York, 1970. · Zbl 0211.06501
[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 · doi:10.1093/qmath/25.1.359
[4] D. G. Northcott: Injective envelopes and inverse polynomials. J. London Math. Soc. (2), 8 (1974), 290-296. · Zbl 0284.13012 · doi:10.1112/jlms/s2-8.2.290
[5] S. Park: Inverse polynomials and injective covers. Comm. Algebra 21 (1993), 4599-4613. · Zbl 0794.16004 · doi:10.1080/00927879308824819
[6] S. Park: The Macaulay-Northcott functor. Arch. Math. (Basel) 63 (1994), 225-230. · Zbl 0804.18009 · doi:10.1007/BF01189824
[7] J. Rotman: An Introduction to Homological Algebra. Academic Press Inc., New York, 1979. · Zbl 0441.18018
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.