Maximal commutative algebras of linear transformations
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- by R. C. Courter
- Trans. Amer. Math. Soc. 101 (1961), 177-199
- DOI: https://doi.org/10.1090/S0002-9947-1961-0130894-9
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References
- H. S. Allen, Commutative rings of linear transformations and infinite matrices, Quart. J. Math. Oxford Ser. (2) 8 (1957), 39–53. MR 85213, DOI 10.1093/qmath/8.1.39
- Emil Artin, Cecil J. Nesbitt, and Robert M. Thrall, Rings with Minimum Condition, University of Michigan Publications in Mathematics, no. 1, University of Michigan Press, Ann Arbor, Mich., 1944. MR 0010543 Bernard Charles, Sur l’algèbre des opérateurs linéaires, J. Math. Pures Appl. vol. 33 (1954) pp. 81-145.
- P. M. Grundy, A generalization of additive ideal theory, Proc. Cambridge Philos. Soc. 38 (1942), 241–279. MR 7392, DOI 10.1017/s0305004100021940
- Paul R. Halmos, Finite-dimensional vector spaces, The University Series in Undergraduate Mathematics, D. Van Nostrand Co., Inc., Princeton-Toronto-New York-London, 1958. 2nd ed. MR 0089819
- Nathan Jacobson, Lectures in Abstract Algebra. Vol. I. Basic Concepts, D. Van Nostrand Co., Inc., Toronto-New York-London, 1951. MR 0041102 —, Lectures in abstract algebra, vol. II, New York, Van Nostrand, 1953.
- N. Jacobson, Schur’s theorems on commutative matrices, Bull. Amer. Math. Soc. 50 (1944), 431–436. MR 10540, DOI 10.1090/S0002-9904-1944-08169-X —, Structure of rings, Amer. Math. Soc. Colloquim Publications, vol. 37, 1956.
- A. G. Kurosh, The theory of groups. Vol. II, Chelsea Publishing Co., New York, N.Y., 1956. Translated from the Russian and edited by K. A. Hirsch. MR 0080089
- D. G. Northcott, Ideal theory, Cambridge Tracts in Mathematics and Mathematical Physics, No. 42, Cambridge, at the University Press, 1953. MR 0058575 I. Schur, Zur Theorie vertauschbaren Matrizen, J. Reine Angew. Math. vol. 30 (1905) pp. 66-76.
- Ernst Snapper, Completely indecomposable modules, Canad. J. Math. 1 (1949), 125–152. MR 29882, DOI 10.4153/cjm-1949-013-3
- D. A. Suprunenko, On maximal commutative subalgebras of the full linear algebra, Uspehi Mat. Nauk (N.S.) 11 (1956), no. 3(69), 181–184 (Russian). MR 0082983
- Oscar Zariski and Pierre Samuel, Commutative algebra, Volume I, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, New Jersey, 1958. With the cooperation of I. S. Cohen. MR 0090581
Bibliographic Information
- © Copyright 1961 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 101 (1961), 177-199
- MSC: Primary 13.60; Secondary 16.00
- DOI: https://doi.org/10.1090/S0002-9947-1961-0130894-9
- MathSciNet review: 0130894