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1	Properties of Some Classical Integral Domains Crawford, Timothy B. 05 1900 (has links) Greatest common divisor domains, Bezout domains, valuation rings, and Prüfer domains are studied. Chapter One gives a brief introduction, statements of definitions, and statements of theorems without proof. In Chapter Two theorems about greatest common divisor domains and characterizations of Bezout domains, valuation rings, and Prüfer domains are proved. Also included are characterizations of a flat overring. Some of the results are that an integral domain is a Prüfer domain if and only if every overring is flat and that every overring of a Prüfer domain is a Prüfer domain. greatest common divisor domains Bezout domains valuation rings Prüfer domains Commutative rings. Ideals (Algebra)
2	On the Conjugacy of Maximal Toral Subalgebras of Certain Infinite-Dimensional Lie Algebras Gontcharov, Aleksandr 10 September 2013 (has links) We will extend the conjugacy problem of maximal toral subalgebras for Lie algebras of the form $\g{g} \otimes_k R$ by considering $R=k[t,t^{-1}]$ and $R=k[t,t^{-1},(t-1)^{-1}]$, where $k$ is an algebraically closed field of characteristic zero and $\g{g}$ is a direct limit Lie algebra. In the process, we study properties of infinite matrices with entries in a B\'zout domain and we also look at how our conjugacy results extend to universal central extensions of the suitable direct limit Lie algebras. Lie algebras representation theory Bezout domains Bezout Rings central extensions conjugacy problem direct limit lie algebras maximal toral subalgebra cartan subalgebra finitely generated bezout domain
3	On the Conjugacy of Maximal Toral Subalgebras of Certain Infinite-Dimensional Lie Algebras Gontcharov, Aleksandr January 2013 (has links) We will extend the conjugacy problem of maximal toral subalgebras for Lie algebras of the form $\g{g} \otimes_k R$ by considering $R=k[t,t^{-1}]$ and $R=k[t,t^{-1},(t-1)^{-1}]$, where $k$ is an algebraically closed field of characteristic zero and $\g{g}$ is a direct limit Lie algebra. In the process, we study properties of infinite matrices with entries in a B\'zout domain and we also look at how our conjugacy results extend to universal central extensions of the suitable direct limit Lie algebras. Lie algebras representation theory Bezout domains Bezout Rings central extensions conjugacy problem direct limit lie algebras maximal toral subalgebra cartan subalgebra finitely generated bezout domain

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