|
Some applications of module theory to functor categories
Author(s):
Barry
Mitchell
Journal:
Bull. Amer. Math. Soc.
84
(1978),
867-885.
MSC (1970):
Primary 18E10, 18H15, 18G20, 13A60, 18G20
MathSciNet review:
0499732
Retrieve article in:
PDF
References |
Similar articles |
Additional information
References:
- 1.
- H. Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466-488. MR 157984
- 2.
- H. Bass, Torsion free and projective modules, Trans. Amer. Math. Soc. 102 (1962), 319-327. MR 140542
- 3.
- H. Bass, Projective modules over free groups are free, J. Algebra 1 (1964), 367-373. MR 178032
- 4.
- J.-E. Björk, Rings satisfying a minimum condition on principal ideals, J. Reine Angew. Math. 236 (1969), 112-119. MR 248165
- 5.
- H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, Princeton, N. J., 1956. MR 77480
- 6.
- C. Cheng and B. Mitchell, Flatness and projecthity of modules that come from C-sets, Algebra, Topology, and Category Theory, Academic Press, New York, 1976, pp. 33-44. MR 409599
- 7.
- C. Cheng and B. Mitchell, DCCposets of cohomological dimension one, J. Pure Appl. Algebra (to appear). MR 506664
- 8.
- C. Cheng, Finite partially ordered set of cohomological dimension one, J. Algebra 40 (1976), 340-347. MR 419564
- 9.
- C. Cheng, Deltas of Hochschild dimension one, Proc. Amer. Math. Soc. 67 (1977), 221-223. MR 476834
- 10.
- P. M. Cohn, Free ideal rings, J. Algebra 1 (1964), 47-69. MR 161891
- 11.
- P. M. Cohn, Free rings and their relations, Academic Press, New York, 1971. MR 371938
- 12.
- S. Eilenberg, A. Rosenberg, and D. Zelinsky, On the dimension of modules and algebras. VIII, Nagoya Math. J. 12 (1957), 71-93. MR 98774
- 13.
- G. Hochschild, Note on relative homological dimension, Nagoya Math J. 13 (1958), 89-94. MR 100015
- 14.
- J. Isbell, Exact colimits. I, Ann. of Math. (2) 100 (1974), 633-637. MR 352200
- 15.
- J. Isbell and B. Mitchell, Exact colimits and fixed points, Trans. Amer. Math. Soc. 220 (1976), 289-298. MR 404377
- 16.
- A. V. Jategaonkar, A counterexample in ring theory and homological algebra, J. Algebra 12 (1969), 418-440. MR 240131
- 17.
- I. Kaplansky, Projective modules, Ann. of Math. (2) 68 (1958), 372-377. MR 100017
- 18.
- D. Latch, On derived functors of limit, Trans. Amer. Math. Soc. 181 (1973), 155-164. MR 323866
- 19.
- D. Latch and B. Mitchell, On the difference between cohomological and homological dimension, J. Pure Appl. Algebra 5 (1974), 333-343. MR 360755
- 20.
- O. Laudal, Note on the projective limit on small categories, Proc. Amer. Math. Soc. 33 (1972), 307-309. MR 291241
- 21.
- D. Lazard, Autour de la platitude, Bull. Soc. Math. France 97 (1969), 81-128. MR 254100
- 22.
- R. C. Lyndon, Cohomology theory of groups with a single defining relation, Ann. of Math. (2) 52 (1950), 650-665. MR 47046
- 23.
- B. Mitchell, On the dimension of objects and categories. I, II, J. Algebra 9 (1968), 314-368 MR 237604
- 24.
- B. Mitchell, Rings with several objects, Advances in Math. 8 (1972), 1-161. MR 294454
- 25.
- B. Mitchell, The dominion of Isbell, Trans. Amer. Math. Soc. 167 (1972), 319-331. MR 294441
- 26.
- B. Mitchell, The cohomological dimension of a directed set, Canad. J. Math. 25. (1973), 233-238. MR 371996
- 27.
- B. Osofsky, Homological dimension and the continuum hypothesis, Trans. Amer. Math. Soc. 132 (1968), 217-230. MR 224606
- 28.
- J. R. Stallings, On torsion free groups with infinitely many ends, Ann. of Math. (2) 88 (1968), 312-334. MR 228573
- 29.
- R. G. Swan, Groups of cohomological dimension one, J. Algebra 12 (1969), 585-610. MR 240177
- 30.
- R. Wong, Monoid rings which are free ideal rings, J. Algebra (to appear).
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(1970):
18E10, 18H15, 18G20, 13A60, 18G20
Retrieve articles in all Journals with MSC
(1970):
18E10, 18H15, 18G20, 13A60, 18G20
Additional Information:
DOI:
10.1090/S0002-9904-1978-14530-3
PII:
S 0002-9904(1978)14530-3
|