JOURNAL BROWSE
Search
Advanced SearchSearch Tips
UNIFORM AND COUNIFORM DIMENSION OF GENERALIZED INVERSE POLYNOMIAL MODULES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
UNIFORM AND COUNIFORM DIMENSION OF GENERALIZED INVERSE POLYNOMIAL MODULES
Zhao, Renyu;
  PDF(new window)
 Abstract
Let M be a right R-module, (S, ) a strictly totally ordered monoid which is also artinian and a monoid homomorphism, and let denote the generalized inverse polynomial module over the skew generalized power series ring [[]]. In this paper, we prove that has the same uniform dimension as its coefficient module , and that if, in addition, R is a right perfect ring and S is a chain monoid, then has the same couniform dimension as its coefficient module .
 Keywords
skew generalized power series ring;generalized inverse polynomial module;uniform dimension;couniform dimension;
 Language
English
 Cited by
1.
Attached prime ideals of generalized inverse polynomial modules, Asian-European Journal of Mathematics, 2017, 10, 02, 1750023  crossref(new windwow)
 References
1.
S. Annin, Associated and attached primes over noncommutative rings, Ph. D. Diss., University of California at Berkeley, 2002.

2.
S. Annin, Couniform dimension over skew polynomial rings, Comm. Algebra 33 (2005), no. 4, 1195-1204. crossref(new window)

3.
M. Ferrero, R. Mazurek, and A. Sant'Ana, On right chain semigroups, J. Algebra 292 (2005), no. 2, 574-584. crossref(new window)

4.
P. Grzeszczuk, Goldie dimension of differential operator rings, Comm. Algebra 16 (1988), no. 4, 689-701. crossref(new window)

5.
T. Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics volume 189, Springer-Verlag, Berlin-Heidelberg-New York, 1999.

6.
Z. K. Liu, Endomorphism rings of modules of generalized inverse polynomials, Comm. Algebra 28 (2000), no. 2, 803-814. crossref(new window)

7.
Z. K. Liu, Injectivity of modules of generalized inverse polynomials, Comm. Algebra 29 (2001), no. 2, 583-592. crossref(new window)

8.
Z. K. Liu, Injective precover and modules of generalized inverse polynomials, Chin. Ann. Math. Ser. B 25 (2004), no. 1, 129-138. crossref(new window)

9.
Z. K. Liu, Triangular matrix representations of rings of generalized power series, Acta Math. Sin. (Engl. Ser.) 22 (2006), no. 4, 989-998. crossref(new window)

10.
Z. K. Liu and H. Cheng, Quasi-duality for the rings of generalized power series, Comm. Algebra 28 (2000), no. 3, 1175-1188. crossref(new window)

11.
Z. K. Liu and Y. Fan, Co-Hopfian modules of generalized inverse polynomials, Acta Math. Sin. (Engl. Ser.) 17 (2001), no. 3, 431-436. crossref(new window)

12.
J. Matczuk, Goldie rank of Ore extensions, Comm. Algebra 23 (1995), no. 4, 1455-1471. crossref(new window)

13.
R. Mazurek and M. Ziembowski, Uniserial rings of skew generalized power series, J. Algebra 318 (2007), no. 2, 737-764. crossref(new window)

14.
A. S. McKerrow, On the injective dimension of modules of power series, Quart. J. Math. Oxford Ser. (2) 25 (1974), 359-368. crossref(new window)

15.
D. G. Northcott, Injective envelopes and inverse polynomials, London Math. Soc. 8 (1974), 290-296. crossref(new window)

16.
S. Park, The Macaulay-Northcott functor, Arch. Math. 63 (1994), no. 3, 225-230. crossref(new window)

17.
S. Park, Inverse polynomials and injective covers, Comm. Algebra 21 (1993), no. 12, 4599-4613. crossref(new window)

18.
P. Ribenboim, Semisimple rings and von Neumann regular rings of generalized power series, J. Algebra 198 (1997), no. 2, 327-338. crossref(new window)

19.
B. Sarath and K. Varadarajan, Dual Goldie dimension II, Comm. Algebra 7 (1979), no. 17, 1885-1899. crossref(new window)

20.
R. C. Shock, Polynomial rings over finite dimensional rings, Pacific J. Math. 42 (1972), 251-257. crossref(new window)

21.
K. Varadarajan, Dual Goldie dimension, Comm. Algebra 7 (1979), no. 6, 565-610. crossref(new window)

22.
K. Varadarajan, On a theorem of Shock, Comm. Algebra 10 (1982), no. 20, 2205-2222. crossref(new window)

23.
K. Varadarajan, Dual Goldie dimension of certain extension rings, Comm. Algebra 10 (1982), no. 20, 2223-2231. crossref(new window)

24.
R. Y. Zhao and Z. K. Liu, Artinness of generalized Macaulay-Northcott modules, Comm. Algebra 37 (2009), no. 2, 525-531. crossref(new window)