Notes on linkage of modules with respect to a semidualizing module

References

• Auslander, M., Bridger, M. (1969). Stable Module Theory. Province, RI: American Mathematical Society.
   Google Scholar
• Bruns, W., Herzog, J. (1998). Cohen-Macaulay Rings. Revised edition. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Celikbas, O., Dibaei, M. T., Gheibi, M., Sadeghi, A, Takahashi, R. (2019). Associated primes and syzygies of linked modules. J. Commut. Algebra. 11(3):301–323. DOI: 10.1216/JCA-2019-11-3-301.
   Web of Science ®Google Scholar
• Christensen, L. W. (2000). Gorenstein Dimensions. Lecture Notes in Mathematics 1747. Berlin: Springer-Verlag.
   Google Scholar
• Christensen, L. W. (2001). Semi-dualizing complexes and their Auslander categories. Trans. Amer. Math. Soc. 353(5):1839–1883. DOI: 10.1090/S0002-9947-01-02627-7.
   Web of Science ®Google Scholar
• Christensen, L. W., Frankild, A., Holm, H. (2006). On Gorenstein projective, injective and flat dimensions: a functorial description with applications. J. Algebra. 302(1):231–279. DOI: 10.1016/j.jalgebra.2005.12.007.
   Web of Science ®Google Scholar
• Dibaei, M. T., Sadeghi, A. (2013). Linkage of finite Gorenstein dimension modules. J. Algebra. 376:261–278. DOI: 10.1016/j.jalgebra.2012.11.035.
   Web of Science ®Google Scholar
• Dibaei, M. T., Sadeghi, A. (2015). Linkage of modules and the Serre conditions. J. Pure Appl. Algebra. 219(10): 4458–4478. DOI: 10.1016/j.jpaa.2015.02.027.
   Web of Science ®Google Scholar
• Dibaei, M. T., Sadeghi, A. (2018). Linkage of modules with respect to a semidualizing module. Pacific J. Math. 294(2):307–328. DOI: 10.2140/pjm.2018.294.307.
   Web of Science ®Google Scholar
• Enochs, E. E., Jenda, O. M. G. (1995). Gorenstein injective and projective modules. Math. Z. 220(4):611–633. DOI: 10.1007/BF02572634.
   Web of Science ®Google Scholar
• Foxby, H. B. (1972). Gorenstein modules and related modules. Math. Scand. 31:267–284. DOI: 10.7146/math.scand.a-11434.
   Web of Science ®Google Scholar
• Foxby, H. B. (1975). Quasi-perfect modules over Cohen-Macaulay rings. Math. Nachr. 66:103–110. DOI: 10.1002/mana.19750660111.
   Web of Science ®Google Scholar
• Geng, Y. (2013). A generalization of the Auslander transpose and the generalized Gorenstein dimension. Czechoslovak Math. J. 63(1):143–156. DOI: 10.1007/s10587-013-0009-1.
   Web of Science ®Google Scholar
• Golod, E. S. (1984). G-dimension and generalized perfect ideals. Trudy Mat. Inst. Steklov. 165:62–66 (Russian).
   Google Scholar
• Golod, E. S. (1985). Uspekhi Mat. Nauk 40(1):234 (Question, in Russian).
   Google Scholar
• Holm, H., J\orgensen, P. (2006). Semi-dualizing modules and related Gorenstein homological dimensions. J. Pure Appl. Algebra. 205(2):423–445. DOI: 10.1016/j.jpaa.2005.07.010.
   Web of Science ®Google Scholar
• Iima, K.-I., Takahashi, R. (2016). Perfect linkage of Cohen-Macaulay modules over Cohen-Macaulay rings. J. Algebra. 458:134–155. DOI: 10.1016/j.jalgebra.2016.03.014.
   Web of Science ®Google Scholar
• Lam, T.Y. (1991). A First Course in Noncommutative Rings. Berlin: Springer-Verlag.
   Google Scholar
• Martin, H. M. (2000). Linkage and the generic homology of modules. Commun. Algebra. 28(9):4285–4301. DOI: 10.1080/00927870008827090.
   Web of Science ®Google Scholar
• Martsinkovsky, A. (2010). 1-torsion of finite modules over semiperfect rings. J. Algebra. 324(10):2595–2607. DOI: 10.1016/j.jalgebra.2010.09.001.
   Web of Science ®Google Scholar
• Martsinkovsky, A., Strooker, J. R. (2004). Linkage of modules. J. Algebra 271(2):587–626. DOI: 10.1016/j.jalgebra.2003.07.020.
   Web of Science ®Google Scholar
• Maşek, V. (2000). Gorenstein dimension and torsion of modules over commutative Noetherian rings. Commun. Algebra. 28(12):5783–5811. DOI: 10.1080/00927870008827189.
   Web of Science ®Google Scholar
• Nagel, U. (2005). Liaison classes of modules. J. Algebra. 284(1):236–272. DOI: 10.1016/j.jalgebra.2004.09.022.
   Web of Science ®Google Scholar
• Nishida, K. (2009). Linkage and duality of modules. Math. J. Okayama Univ. 51:71–81. DOI: 10.18926/mjou/33220.
   Google Scholar
• Peskine, C., Szpiro, L. (1974). Liaison des variétés algébriques. I. Invent. Math. 26:271–302. DOI: 10.1007/BF01425554.
   Web of Science ®Google Scholar
• Sadeghi, A. (2017). Linkage of finite GC-dimension modules. J. Pure Appl. Algebra. 221(6):1344–1365. DOI: 10.1016/j.jpaa.2016.09.015.
   Google Scholar
• Sadeghi, A. (2019). Notes on linkage of modules. Proc. Edinb. Math. Soc. 62(4):1045–1062. DOI: 10.1017/S0.013091519000117.
   Web of Science ®Google Scholar
• Salimi, M., Sather-Wagstaff, S., Tavasoli, E., Yassemi, S. (2014). Relative Tor functors with respect to a semidualizing module. Algebras Represent. Theory. 17(1): 103–120. DOI: 10.1007/s10468-012-9389-4.
   Web of Science ®Google Scholar
• Salimi, M., Tavasoli, E., Yassemi, S. (2012). Top local cohomology modules and Gorenstein injectivity with respect to a semidualizing module. Arch. Math (Basel). 98(4):299–305. DOI: 10.1007/s00013-012-0371-5.
   Web of Science ®Google Scholar
• Salimi, M., Tavasoli, E., Moradifar, P., Yassemi, S. (2014). Syzygy and torsionless modules with respect to a semidualizing module. Algebr. Represent. Theory. 17(4):1217–1234. DOI: 10.1007/s10468-013-9443-x.
   Web of Science ®Google Scholar
• Salimi, M., Tavasoli, E., Yassemi, S. (2015). Reflexive modules with finite Gorenstein dimension with respect to a semidualizing module. Proc. Indian Acad. Sci. Math. Sci. 125(1):21–28. DOI: 10.1007/s12044-015-0218-7.
   Google Scholar
• Sather-Wagstaff, S. Semidualizing modules. https://www.ndsu.edu/pubweb/∼ssatherw/DOCS/sdm.pdf
   Google Scholar
• Sather-Wagstaff, S., Sharif, T., White, D. (2010). Comparison of relative cohomology theories with respect to semidualizing modules. Math. Z. 264(3):571–600. DOI: 10.1007/s00209-009-0480-4.
   Web of Science ®Google Scholar
• Sather-Wagstaff, S., Sharif, T., White, D. (2010). Tate cohomology with respect to semidualizing modules. J. Algebra. 324(9):2336–2368. DOI: 10.1016/j.jalgebra.2010.07.007.
   Web of Science ®Google Scholar
• Sather-Wagstaff, S., Yassemi, S. (2009). Modules of finite homological dimension with respect to a semidualizing module. Arch. Math. (Basel). 93(2):111–121. DOI: 10.1007/s00013-009-0020-9.
   Web of Science ®Google Scholar
• Takahashi, R., White, D. (2010). Homological aspects of semidualizing modules. Math. Scand. 106(1)5–22. DOI: 10.7146/math.scand.a-15121.
   Web of Science ®Google Scholar
• Vasconcelos, W. V. (1974). Divisor Theory in Module Categories. North-Holland Math. Studies 14, Notas de Matemática 53. Amsterdam, NH: North-Holland Publishing Company.
   Google Scholar
• Vasconcelos, W. V. (1968). Reflexive modules over Gorenstein rings. Proc. Amer. Math. Soc. 19:1349–1355. DOI: 10.1090/S0002-9939-1968-0237480-2.
   Web of Science ®Google Scholar
• White, D. (2010). Gorenstein projective dimension with respect to a semidualizing module. J. Commut. Algebra. 2(1):111–137. DOI: 10.1216/JCA-2010-2-1-111.
   Web of Science ®Google Scholar
• Yoshino, Y., Isogawa, S. (2000). Linkage of Cohen-Macaulay modules over a Gorenstein ring. J. Pure Appl. Algebra. 149(3):305–318. DOI: 10.1016/S0022-4049(98)00167-4.
   Web of Science ®Google Scholar