Kubik, Bethany Quasidualizing modules. (English) Zbl 1304.13031 J. Commut. Algebra 6, No. 2, 209-229 (2014). Let \(A\) be a commutative noetherian local ring. An \(A\)-module of finite type \(C\) is called semidualizing if the homothety homomorphism \(A \to \)Hom\(_A(C,C)\) is an isomorphism and Ext\(^{>0}_A(C,C)=0\). In this paper the Matlis duals of semidualizing modules are identified as the artinian modules \(M\) such that \(\hat{A} \to \)Hom\(_A(M,M)\) is an isomorphism and Ext\(^{>0}_A(M,M)=0\), where \(\hat{A}\) is the completion of the local ring \(A\). Some properties and variants are also explored. Reviewer: Javier Majadas (Santiago de Compostela) Cited in 5 Documents MSC: 13D07 Homological functors on modules of commutative rings (Tor, Ext, etc.) 13E10 Commutative Artinian rings and modules, finite-dimensional algebras 13J10 Complete rings, completion Keywords:quasidualizing; semidualizing; matlis duality × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid References: [1] M.F. Atiyah and I.G. Macdonald, Introduction to commutative algebra , Addison-Wesley Publishing Co., Reading, MA, 1969. · Zbl 0175.03601 [2] M.P. Brodmann and R.Y. Sharp, Local cohomology : An algebraic introduction with geometric applications , Cambr. Stud. Adv. Math. 60 , Cambridge University Press, Cambridge, 1998. · Zbl 0903.13006 [3] E.E. Enochs and O.M.G. Jenda, Relative homological algebra , de Gruyter Expos. Math. 30 , Walter de Gruyter & Co., Berlin, 2000. · Zbl 0952.13001 [4] H. Holm and D. White, Foxby equivalence over associative rings , J. Math. Kyoto Univ. 47 (2007), 781-808. · Zbl 1154.16007 [5] T. Ishikawa, On injective modules and flat modules , J. Math. Soc. Jap. 17 (1965), 291-296. · Zbl 0199.07802 · doi:10.2969/jmsj/01730291 [6] B. Kubik, M.J. Leamer and S. Sather-Wagstaff, Homology of artinian and mini-max modules , I, J. Pure Appl. Alg. 215 (2011), 2486-2503. · Zbl 1232.13008 · doi:10.1016/j.jpaa.2011.02.007 [7] H. Matsumura, Commutative ring theory , second ed., Stud. Adv. Math. 8 , University Press, Cambridge, 1989. · Zbl 0666.13002 [8] Joseph J. Rotman, An introduction to homological algebra , second ed., Universitext, Springer, New York, 2009. · Zbl 1157.18001 [9] W.V. Vasconcelos, Divisor theory in module categories , North-Holland Publishing Co., Amsterdam, 1974. · Zbl 0296.13005 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.