Nearly prime subsemigroups ofβℕ |
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| Authors: | Neil Hindman Dona Strauss |
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| Institution: | (1) Department of Mathematics, Howard University, 20059 Washington, DC, USA;(2) Department of Pure Mathematics, University of Hull, HU6 7RX Hull, United Kingdom |
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| Abstract: | We show that there exist relatively small subsemigroupsM ofβℕ with the property that ifp+q andq+p are inM then bothp andq are inM + ℤ. We also show that it is consistent with the usual axioms of set theory that there is some idempotent e inβℕ such that ifp+q=e, then bothp andq are ine + ℤ.
The first author acknowledges support received from the National Science Foundation (USA) via grant DMS90-25025. |
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