Embedding countable rings in $2$-generator rings
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- by K. C. O’Meara
- Proc. Amer. Math. Soc. 100 (1987), 21-24
- DOI: https://doi.org/10.1090/S0002-9939-1987-0883394-6
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Abstract:
A short elementary proof involving matrices is used to show that any countable ring can be embedded in a $2$-generator ring. Immediate corollaries are the known results that any countable (respectively finite) semigroup can be embedded in a $2$-generator (respectively finite $2$-generator) semigroup.References
- Trevor Evans, Embedding theorems for multiplicative systems and projective geometries, Proc. Amer. Math. Soc. 3 (1952), 614–620. MR 0050566, DOI 10.1090/S0002-9939-1952-0050566-9
- Graham Higman, B. H. Neumann, and Hanna Neumann, Embedding theorems for groups, J. London Math. Soc. 24 (1949), 247–254. MR 32641, DOI 10.1112/jlms/s1-24.4.247
- B. H. Neumann, Embedding theorems for semigroups, J. London Math. Soc. 35 (1960), 184–192. MR 163969, DOI 10.1112/jlms/s1-35.2.184
- Saraswathi Subbiah, Another proof of a theorem of Evans, Semigroup Forum 6 (1973), no. 1, 93–94. MR 376930, DOI 10.1007/BF02389113 Solution #6244 to the problem proposed by John Myhill, Amer. Math. Monthly 87 (1980), 676-678.
Bibliographic Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 21-24
- MSC: Primary 16A56; Secondary 16A42, 16A44, 20M05
- DOI: https://doi.org/10.1090/S0002-9939-1987-0883394-6
- MathSciNet review: 883394