Some Consequences of Schanuel's Conjecture in Exponential Rings

摘要

In last years Schanuel's Conjecture has played a fundamental role in Transcendental Number Theory and in decidability issues.In this article we investigate algebraic relations among the elements of the exponential field (, e x ) modulo Schanuel's Conjecture. We prove that there are no further relations between π and i assuming Schanuel's Conjecture except the known ones, e πi  = −1 and i 2 = −1. Moreover, modulo Schanuel's Conjecture we prove that the E-subring of generated by π is isomorphic to the free exponential ring on π.View full textDownload full textKey WordsExponential rings, Schanuel's Conjecture2000 Mathematics Subject Classification03C60, 03C98Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/00927870701410694