Results 1 to 10 of about 178 (83)
Separating 𝑝-bases and transcendental extension fields [PDF]
Proceedings of the American Mathematical Society, 1972 Let L / K L/K denote an extension field of characteristic p ≠ 0 p \ne 0 . It is known that if L / K L/K has a finite separating transcendence base, then every relative p p -base of
Mordeson, J. N., Vinograde, B.
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Transcendental Extensions of Field Topologies on Countable Fields [PDF]
Proceedings of the American Mathematical Society, 1973 Let be a field topology on a countable field K and let K(x) be a simple transcendental extension of K. Then there exists a field topology 9' for K(x) such that 'l K=Y. Let K be a countable field and let 91 be a fundamental system of neighborhoods at zero.
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A structure theorem for simple transcendental extensions of valued fields [PDF]
Proceedings of the American Mathematical Society, 1988 The fundamental inequality for a finite algebraic extension of a valued field relates the degree of the extension to the ramification indices and residue degrees, and of primary importance is the question of when this inequality becomes equality.
Matignon, Michel, Ohm, Jack
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Simple transcendental extensions of valued fields II: A fundamental inequality
Kyoto Journal of Mathematics, 1985 Let \(K_ 0\subset K=K_ 0(x)\) be fields with x transcendental over \(K_ 0:\) let \(v_ 0\) be a valuation of \(K_ 0\) and v be an extension of \(v_ 0\) to K; and let \(V_ 0\subset V\), \(k_ 0\subset k\), and \(G_ 0\subset G\) be the respective valuation rings, residue fields, and value groups. This paper is concerned with extensions such that \(k/k_ 0\)
Matignon, Michel, Ohm, Jack
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Graded transcendental extensions of graded fields [PDF]
International Journal of Mathematics and Mathematical Sciences, 2003 We study transcendency properties for graded field extension and give an application to valued field extensions.
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On almost simple transcendental field extensions
International Journal of Algebra, 2015 We study some properties of almost simple transcendental eld extensions in order to analyze the endomorphisms ring of algebraically bounded modules where is a semigenerically tame nite-dimensional k algebra, k a perfect eld.
Antonio Gonzalez Fernandez +2 more
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Rendiconti del Seminario Matematico della Università di Padova, 2020 Let (K, |\cdot|) be a local field. In this paper we define an invariant analogous to the discriminant over K for certain transcendental elements over
Achimescu, S. +2 more
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Conservation of the noetherianity by perfect transcendental field extensions
Revista Matemática Iberoamericana, 2003 Let k be a perfect field of characteristic p>0 , k(t)_{per} the perfect ...
Fernández-Lebrón, Magdalena +1 more
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The ruled residue theorem for simple transcendental extensions of valued fields [PDF]
Proceedings of the American Mathematical Society, 1983 A proof is given for the Ruled Residue Conjecture, which asserts that if υ \upsilon is a valuation of a simple transcendental field extension K 0 ( x ) {K_0}(x) and υ 0 {\upsilon _0} is ...
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A uniqueness problem in simple transcendental extensions of valued fields [PDF]
Proceedings of the Edinburgh Mathematical Society, 1994 Let υ0 be a valuation of a field K0 with value group G0 and υ be an extension of υ0 to a simple transcendental extension K0(x) having value group G such that G/G0 is not a torsion group. In this paper we investigate whether there exists t∈K0(x)/K0 with υ(t) non-torsion mod G0 such that υ is the unique extension to K0(x) of its restriction to the ...
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