참고문헌
- S. Annin, Associated and attached primes over noncommutative rings, Ph. D. Diss., University of California at Berkeley, 2002.
- S. Annin, Couniform dimension over skew polynomial rings, Comm. Algebra 33 (2005), no. 4, 1195-1204. https://doi.org/10.1081/AGB-200053947
- M. Ferrero, R. Mazurek, and A. Sant'Ana, On right chain semigroups, J. Algebra 292 (2005), no. 2, 574-584. https://doi.org/10.1016/j.jalgebra.2005.07.019
- P. Grzeszczuk, Goldie dimension of differential operator rings, Comm. Algebra 16 (1988), no. 4, 689-701. https://doi.org/10.1080/00927878808823596
- T. Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics volume 189, Springer-Verlag, Berlin-Heidelberg-New York, 1999.
- Z. K. Liu, Endomorphism rings of modules of generalized inverse polynomials, Comm. Algebra 28 (2000), no. 2, 803-814. https://doi.org/10.1080/00927870008826861
- Z. K. Liu, Injectivity of modules of generalized inverse polynomials, Comm. Algebra 29 (2001), no. 2, 583-592. https://doi.org/10.1081/AGB-100001525
- Z. K. Liu, Injective precover and modules of generalized inverse polynomials, Chin. Ann. Math. Ser. B 25 (2004), no. 1, 129-138. https://doi.org/10.1142/S0252959904000135
- Z. K. Liu, Triangular matrix representations of rings of generalized power series, Acta Math. Sin. (Engl. Ser.) 22 (2006), no. 4, 989-998. https://doi.org/10.1007/s10114-005-0555-z
- Z. K. Liu and H. Cheng, Quasi-duality for the rings of generalized power series, Comm. Algebra 28 (2000), no. 3, 1175-1188. https://doi.org/10.1080/00927870008826888
- Z. K. Liu and Y. Fan, Co-Hopfian modules of generalized inverse polynomials, Acta Math. Sin. (Engl. Ser.) 17 (2001), no. 3, 431-436. https://doi.org/10.1007/s101140000044
- J. Matczuk, Goldie rank of Ore extensions, Comm. Algebra 23 (1995), no. 4, 1455-1471. https://doi.org/10.1080/00927879508825287
- R. Mazurek and M. Ziembowski, Uniserial rings of skew generalized power series, J. Algebra 318 (2007), no. 2, 737-764. https://doi.org/10.1016/j.jalgebra.2007.08.024
- A. S. McKerrow, On the injective dimension of modules of power series, Quart. J. Math. Oxford Ser. (2) 25 (1974), 359-368. https://doi.org/10.1093/qmath/25.1.359
- D. G. Northcott, Injective envelopes and inverse polynomials, London Math. Soc. 8 (1974), 290-296. https://doi.org/10.1112/jlms/s2-8.2.290
- S. Park, The Macaulay-Northcott functor, Arch. Math. 63 (1994), no. 3, 225-230. https://doi.org/10.1007/BF01189824
- S. Park, Inverse polynomials and injective covers, Comm. Algebra 21 (1993), no. 12, 4599-4613. https://doi.org/10.1080/00927879308824819
- P. Ribenboim, Semisimple rings and von Neumann regular rings of generalized power series, J. Algebra 198 (1997), no. 2, 327-338. https://doi.org/10.1006/jabr.1997.7063
- B. Sarath and K. Varadarajan, Dual Goldie dimension II, Comm. Algebra 7 (1979), no. 17, 1885-1899. https://doi.org/10.1080/00927877908822434
- R. C. Shock, Polynomial rings over finite dimensional rings, Pacific J. Math. 42 (1972), 251-257. https://doi.org/10.2140/pjm.1972.42.251
- K. Varadarajan, Dual Goldie dimension, Comm. Algebra 7 (1979), no. 6, 565-610. https://doi.org/10.1080/00927877908822364
- K. Varadarajan, On a theorem of Shock, Comm. Algebra 10 (1982), no. 20, 2205-2222. https://doi.org/10.1080/00927878208822830
- K. Varadarajan, Dual Goldie dimension of certain extension rings, Comm. Algebra 10 (1982), no. 20, 2223-2231. https://doi.org/10.1080/00927878208822831
- R. Y. Zhao and Z. K. Liu, Artinness of generalized Macaulay-Northcott modules, Comm. Algebra 37 (2009), no. 2, 525-531. https://doi.org/10.1080/00927870802251112
피인용 문헌
- Attached prime ideals of generalized inverse polynomial modules vol.10, pp.02, 2017, https://doi.org/10.1142/S1793557117500231