1 |
F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, second edition, Graduate Texts in Mathematics, 13, Springer-Verlag, New York, 1992. https://doi.org/10.1007/978-1-4612-4418-9
|
2 |
G. Baccella, Semi-Artinian V-rings and semi-Artinian von Neumann regular rings, J. Algebra 173 (1995), no. 3, 587-612. https://doi.org/10.1006/jabr.1995.1104
DOI
|
3 |
G. Baccella, Exchange property and the natural preorder between simple modules over semi-Artinian rings, J. Algebra 253 (2002), no. 1, 133-166. https://doi.org/10.1016/S0021-8693(02)00044-3
DOI
|
4 |
H. Bass, K-theory and stable algebra, Inst. Hautes Etudes Sci. Publ. Math. No. 22 (1964), 5-60.
|
5 |
H. Chen, Rings with many idempotents, Int. J. Math. Math. Sci. 22 (1999), no. 3, 547-558. https://doi.org/10.1155/S0161171299225471
DOI
|
6 |
D. Estes and J. Ohm, Stable range in commutative rings, J. Algebra 7 (1967), 343-362. https://doi.org/10.1016/0021-8693(67)90075-0
DOI
|
7 |
M. A. Fortes Escalona, I. de las Penas Cabrera, and E. Sanchez Campos, Lifting idempotents in associative pairs, J. Algebra 222 (1999), no. 2, 511-523. https://doi.org/10.1006/jabr.1999.8025
DOI
|
8 |
L. Fuchs, On a substitution property of modules, Monatsh. Math. 75 (1971), 198-204. https://doi.org/10.1007/BF01299099
DOI
|
9 |
S. Garg, H. K. Grover, and D. Khurana, Perspective rings, J. Algebra 415 (2014), 1-12. https://doi.org/10.1016/j.jalgebra.2013.09.055
DOI
|
10 |
K. R. Goodearl, von Neumann Regular Rings, second edition, Robert E. Krieger Publishing Co., Inc., Malabar, FL, 1991.
|
11 |
D. Khurana and T. Y. Lam, Clean matrices and unit-regular matrices, J. Algebra 280 (2004), no. 2, 683-698. https://doi.org/10.1016/j.jalgebra.2004.04.019
DOI
|
12 |
M. Henriksen, On a class of regular rings that are elementary divisor rings, Arch. Math. (Basel) 24 (1973), 133-141. https://doi.org/10.1007/BF01228189
DOI
|
13 |
V. A. Hiremath and S. Hegde, Using ideals to provide a unified approach to uniquely clean rings, J. Aust. Math. Soc. 96 (2014), no. 2, 258-274. https://doi.org/10.1017/S1446788713000591
DOI
|
14 |
I. Kaplansky, Bass's first stable range condition, mimeographed notes, 1971.
|
15 |
D. Khurana and T. Y. Lam, Rings with internal cancellation, J. Algebra 284 (2005), no. 1, 203-235. https://doi.org/10.1016/j.jalgebra.2004.07.032
DOI
|
16 |
P. Menal and J. Moncasi, Lifting units in self-injective rings and an index theory for Rickart -algebras, Pacific J. Math. 126 (1987), no. 2, 295-329. http://projecteuclid.org/euclid.pjm/1102699806
DOI
|
17 |
D. Khurana, T. Y. Lam, and P. P. Nielsen, An ensemble of idempotent lifting hypotheses, J. Pure Appl. Algebra 222 (2018), no. 6, 1489-1511. https://doi.org/10.1016/j.jpaa.2017.07.008
DOI
|
18 |
T. Y. Lam, A crash course on stable range, cancellation, substitution, and exchange, J. Algebra Appl. 3 (2004), 301-343. https://doi.org/10.1142/S0219498804000897
DOI
|
19 |
P. Menal and J. Moncasi, On regular rings with stable range 2, J. Pure Appl. Algebra 24 (1982), no. 1, 25-40. https://doi.org/10.1016/0022-4049(82)90056-1
DOI
|
20 |
W. K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc. 229 (1977), 269-278. https://doi.org/10.2307/1998510
DOI
|
21 |
A. C. Ozcan, A. Harmanci, and P. F. Smith, Duo modules, Glasg. Math. J. 48 (2006), no. 3, 533-545. https://doi.org/10.1017/S0017089506003260
DOI
|
22 |
Z.Wang, J. Chen, D. Khurana, and T.Y. Lam, Rings of idempotent stable range one, Algebr. Represent. Theory 15 (2012), no. 1, 195-200. https://doi.org/10.1007/s10468-011-9276-4
DOI
|
23 |
F. Perera, Lifting units modulo exchange ideals and C*-algebras with real rank zero, J. Reine Angew. Math. 522 (2000), 51-62. https://doi.org/10.1515/crll.2000.040
|
24 |
F. Siddique, On two questions of Nicholson, https://arxiv.org/pdf/1402.4706.pdf, (2014), 5 pages.
|
25 |
J. Ster, Lifting units in clean rings, J. Algebra 381 (2013), 200-208. https://doi.org/10.1016/j.jalgebra.2013.02.014
DOI
|
26 |
L. N. Vaserstein, The stable range of rings and the dimension of topological spaces, Funkcional. Anal. i Prilozen. 5 (1971), no. 2, 17-27.
|
27 |
L. N. Vaserstein, Bass's first stable range condition, J. Pure Appl. Algebra 34 (1984), no. 2-3, 319-330. https://doi.org/10.1016/0022-4049(84)90044-6
DOI
|
28 |
C. A. Weibel, The K-book, Graduate Studies in Mathematics, 145, American Mathematical Society, Providence, RI, 2013.
|
29 |
H.-P. Yu, On quasi-duo rings, Glasgow Math. J. 37 (1995), no. 1, 21-31. https://doi.org/10.1017/S0017089500030342
DOI
|
30 |
Y. Zhou, Generalizations of perfect, semiperfect, and semiregular rings, Algebra Colloq. 7 (2000), no. 3, 305-318. https://doi.org/10.1007/s10011-000-0305-9
DOI
|