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.
- [1] Frank Castagna, Sums of automorphisms of a primary abelian group, Pacific J. Math. 27 (1968), 463–473. MR 0237639
- [2] Irving Kaplansky, Infinite abelian groups, Revised edition, The University of Michigan Press, Ann Arbor, Mich., 1969. MR 0233887
- [3] R. S. Pierce, Endomorphism rings of primary Abelian groups, Proc. Colloq. Abelian Groups (Tihany, 1963) Akadémiai Kiadó, Budapest, 1964, pp. 125–137. MR 0172922
- [4] R. S. Pierce, Homomorphisms of primary abelian groups, Topics in Abelian Groups (Proc. Sympos., New Mexico State Univ., 1962), Scott, Foresman and Co., Chicago, Ill., 1963, pp. 215–310. MR 0177035
- [5] R. W. Stringall, Decompositions of Abelian 𝑝-groups, Proc. Amer. Math. Soc. 28 (1971), 409–410. MR 0274582, https://doi.org/10.1090/S0002-9939-1971-0274582-9
-groups, Proc. Amer. Math. Soc. 28 (1971), 409-410.
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
