The general structure of inverse polynomial modules

Sangwon Park

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 2, page 343-349
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Park, Sangwon. "The general structure of inverse polynomial modules." Czechoslovak Mathematical Journal 51.2 (2001): 343-349. <http://eudml.org/doc/30638>.

@article{Park2001,
abstract = {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.},
author = {Park, Sangwon},
journal = {Czechoslovak Mathematical Journal},
keywords = {module; inverse polynomial; homological dimensions; Hom; Ext; Tor; injective dimension; inverse polynomial modules; homological dimensions; Hom; Ext; Tor; flat dimension; projective dimension},
language = {eng},
number = {2},
pages = {343-349},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The general structure of inverse polynomial modules},
url = {http://eudml.org/doc/30638},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Park, Sangwon
TI - The general structure of inverse polynomial modules
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 2
SP - 343
EP - 349
AB - 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.
LA - eng
KW - module; inverse polynomial; homological dimensions; Hom; Ext; Tor; injective dimension; inverse polynomial modules; homological dimensions; Hom; Ext; Tor; flat dimension; projective dimension
UR - http://eudml.org/doc/30638
ER -

References

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  1. The algebraic theory of modular system, Cambridge Tracts in Math. 19 (1916). (1916) 
  2. Commutative Algebra, W. A. Benjamin, Inc., New York, 1970. (1970) Zbl0211.06501MR0266911
  3. 10.1093/qmath/25.1.359, Quart J.  Math. Oxford Ser. (2), 25 (1974), 359–368. (1974) Zbl0302.16027MR0371881DOI10.1093/qmath/25.1.359
  4. Injective envelopes and inverse polynomials, J. London Math. Soc. (2), 8 (1974), 290–296. (1974) Zbl0284.13012MR0360555
  5. 10.1080/00927879308824819, Comm. Algebra 21 (1993), 4599–4613. (1993) Zbl0794.16004MR1242851DOI10.1080/00927879308824819
  6. 10.1007/BF01189824, Arch. Math. (Basel) 63 (1994), 225–230. (1994) Zbl0804.18009MR1287251DOI10.1007/BF01189824
  7. An Introduction to Homological Algebra, Academic Press Inc., New York, 1979. (1979) Zbl0441.18018MR0538169

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