Primary modules determined by indecomposable idempotent endomorphisms.
Author:
Robert W. Stringall
Journal:
Proc. Amer. Math. Soc. 31 (1972), 54-56
DOI:
https://doi.org/10.1090/S0002-9939-1972-0285608-1
MathSciNet review:
0285608
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Abstract | References | Additional Information
Abstract: A faithful primary module over a complete discrete valuation ring is determined up to isomorphism by any subring of the endomorphism ring of the module which contains all the indecomposable indempotent endomorphisms.
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- [2] I. Kaplansky, Infinite abelian groups, rev. ed., Univ. of Michigan Press, Ann Arbor, Mich., 1969. MR 38 #2208. MR 0233887 (38:2208)
- [3] R. S. Pierce, Endomorphism rings of primary Abelian groups, Proc. Colloq. Abelian Groups (Tihany, 1963), Akad. Kiadó, Budapest, 1964, pp. 125-137. MR 30 #3137. MR 0172922 (30:3137)
- [4] -, Homomorphisms of primary abelian groups, Proc. Sympos. Topics in Abelian Groups (New Mexico State Univ., 1962), Scott, Foresman, Chicago, Ill., 1963, pp. 215-310. MR 31 #1299. MR 0177035 (31:1299)
- [5]
R. Stringall, Decompositions of Abelian
-groups, Proc. Amer. Math. Soc. 28 (1971), 409-410. MR 0274582 (43:345)
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1972-0285608-1
Keywords:
Faithful primary modules over complete discrete valuation rings,
subring generated by idempotent endomorphisms,
subring generated by automorphisms
Article copyright:
© Copyright 1972
American Mathematical Society
