Journal of Commutative Algebra

Semidualizing modules and rings of invariants

William Sanders

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We show there exist no nontrivial semidualizing modules for nonmodular rings of invariants of order $p^n$ with $p$ a prime.

Article information

J. Commut. Algebra, Volume 7, Number 3 (2015), 411-422.

First available in Project Euclid: 14 December 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13A50: Actions of groups on commutative rings; invariant theory [See also 14L24] 13C13: Other special types

Invariant theory semidualizing module rational singularity


Sanders, William. Semidualizing modules and rings of invariants. J. Commut. Algebra 7 (2015), no. 3, 411--422. doi:10.1216/JCA-2015-7-3-411.

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  • Tokuji Araya and Ryo Takahashi, A generalization of a theorem of Foxby, Arch. Math. (Basel) 93 (2009), 123-–127.
  • D.J. Benson, Polynomial invariants of finite groups, Lond. Math. Soc. Lect. Note Series 190, Cambridge University Press, Cambridge, 1993.
  • Lars Winther Christensen and Sean Sather-Wagstaff, A Cohen-Macaulay algebra has only finitely many semidualizing modules, Math. Proc. Cambr. Phil. Soc. 145 (2008), 601-–603.
  • Hailong Dao and Olgur Celikbas, Necessary conditions for the depth formula over cohen-macaulay local rings, 2011, arXiv:1008.2573.
  • Hans-Bjørn Foxby, Gorenstein modules and related modules, Math. Scand. 31 (1973), 267-–284.
  • A. Gerko, On the structure of the set of semidualizing complexes, Illinois J. Math. 48 (2004), 965-–976.
  • A.A. Gerko, Homological dimensions and semidualizing complexes, Sov. Mat. Pril. 30 (2005), 3–30.
  • Shiro Goto, Ryo Takahashi, Naoki Taniguchi and Hoang Le Truong, Huneke-wiegand conjecture and change of rings, 2013, arXiv:1305.4238v2.
  • David A. Jorgensen, Graham J. Leuschke and Sean Sather-Wagstaff, Presentations of rings with non-trivial semidualizing modules, Coll. Math. 63 (2012), 165-–180.
  • Saeed Nasseh and Sean Sather-Wagstaff, A local ring has only finitely many semidualizing complexes up to shift-isomorphism, 2012, arXiv:1201.0037.
  • Sean Sather-Wagstaff, Semidualizing modules and the divisor class group, Illinois J. Math. 51 (2007), 255-–285.
  • ––––, Bass numbers and semidualizing complexes, Commutative algebra and its applications, Walter de Gruyter, Berlin, 2009, 349–-381.
  • ––––, Semidualizing modules, 2009, ssatherw/DOCS/han.pdf.
  • Masataka Tomari and Keiichi Watanabe, Normal $Z_r$-graded rings and normal cyclic covers, Manuscr. Math. 76 (1992), 325-–340.
  • Wolmer V. Vasconcelos, Divisor theory in module categories, North-Holland Publishing Co., Amsterdam, 1974.