Decompositions of Abelian $p$-groups
HTML articles powered by AMS MathViewer
- by R. W. Stringall PDF
- Proc. Amer. Math. Soc. 28 (1971), 409-410 Request permission
Abstract:
Using some elementary properties of endomorphism rings and their radical ideals, an equivalence between the category of $p$-rings and the category of Boolean rings and some examples introduced by the author, it is shown that for every countable atomic Boolean algebra there is a $p$-group without elements of infinite height, standard basic subgroup and no proper isomorphic subgroups which contains a maximal lattice of summands isomorphic to the given Boolean algebra. Moreover, it is established that this lattice is representative in the sense that it determines, up to isomorphism, all the summands of the group.References
- Nathan Jacobson, Structure of rings, American Mathematical Society Colloquium Publications, Vol. 37, American Mathematical Society, 190 Hope Street, Providence, R.I., 1956. MR 0081264, DOI 10.1090/coll/037
- N. H. McCoy and Deane Montgomery, A representation of generalized Boolean rings, Duke Math. J. 3 (1937), no. 3, 455–459. MR 1546001, DOI 10.1215/S0012-7094-37-00335-1
- Roman Sikorski, Boolean algebras, 3rd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 25, Springer-Verlag New York, Inc., New York, 1969. MR 0242724, DOI 10.1007/978-3-642-85820-8
- Robert W. Stringall, Endomorphism rings of primary abelian groups, Pacific J. Math. 20 (1967), 535–557. MR 207830, DOI 10.2140/pjm.1967.20.535 —, The categories of $p$-rings are equivalent, Proc. Amer. Math. Soc. (to appear).
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 409-410
- MSC: Primary 20.30
- DOI: https://doi.org/10.1090/S0002-9939-1971-0274582-9
- MathSciNet review: 0274582