http://math.usask.ca/~fvk/Kapl.pdf WebbABSTRACT. We provide an almost purely algebraic proof of Kaplansky's re-finement of the Gelfand-Mazur theorem asserting that the reals, complex, and quaternions are the only associative normed real algebras with no nonzero topo-logical divisors of zero. 1. INTRODUCTION The Gelfand-Mazur theorem asserts that, if A is an associative …

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WebbKaplansky’s Theorem Let R be a commutative ring with identity. Lemma 1. Suppose U is maximal among ideals of R that are not principal. Then U must be prime. Proof. … Webb1 jan. 1994 · The comparable elements were introduced and studied in [5] to prove, in case of valuation domains, a Kaplansky-type theorem (recall that Kaplansky proved that … birthing companions

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WebbThe following theorem generalizes work by Abrams-Bell-Rangaswamy and Larki: Theorem (L., Lundstrom, Oinert, Wagner 2024)¨ Let L R(E) be a Leavitt path algebra over a unital ring R. Then L R(E) is prime if and only if R is prime and E satisfied Condition (MT-3). Example Take E := A n in the above theorem. Then L R(A n) ∼=M WebbSchool of Mathematics School of Mathematics Webbthese results are based on the Mittag{Le er theorem on inverse limits of complete metric spaces, that we will present in section 2. The Mittag{Le er theorem implies the Baire … daphne daybed with trundle