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Formalized Mathematics, 2021 Summary In this article we further develop field theory in Mizar [1], [2], [3] towards splitting fields. We deal with algebraic extensions [4], [5]: a field extension E of a field F is algebraic, if every element of
Christoph Schwarzweller +1 more
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Generators and number fields for torsion points of a special elliptic curve [PDF]
Arab Journal of Mathematical Sciences, 2020 Let E be an elliptic curve with Weierstrass form y2=x3−px, where p is a prime number and let E[m] be its m-torsion subgroup. Let p1=(x1,y1) and p2=(x2,y2) be a basis for E[m], then we prove that ℚ(E[m])=ℚ(x1,x2,ξm,y1) in general.
Hasan Sankari, Mustafa Bojakli
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Basic Core Fuzzy Logics and Algebraic Routley–Meyer-Style Semantics
Axioms, 2021 Recently, algebraic Routley–Meyer-style semantics was introduced for basic substructural logics. This paper extends it to fuzzy logics. First, we recall the basic substructural core fuzzy logic MIAL (Mianorm logic) and its axiomatic extensions, together ...
Eunsuk Yang
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On The Roots of Unity in Several Complex Neutrosophic Rings [PDF]
Neutrosophic Sets and Systems, 2023 Roots of unity play a basic role in the theory of algebraic extensions of fields and rings. The aim of this paper is to obtain an algorithm to find all n-th roots of unity in five different kinds of neutrosophic complex rings, where many theorems and ...
Djamal Lhiani +3 more
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Extensions of associative algebras [PDF]
Communications in Contemporary Mathematics, 2014 In this paper, we translate the problem of extending an associative algebra by another associative algebra into the language of codifferentials. The authors have been constructing moduli spaces of algebras and studying their structure by constructing their versal deformations. The codifferential language is very useful for this purpose.
Fialowski, A., Penkava, M.
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On extensions of Cayley algebras [PDF]
Proceedings of the American Mathematical Society, 1966 In this note the authors prove the following theorem: Let \(A\) be an alternative algebra over \(F\) and \(B\) any subalgebra with identity \(e\). Then consider the following conditions. (i) There exists \(x, y\in B\), \(\alpha\in F\) such that \(e = \alpha(x, y)^4\), where \((x, y) = xy - yx\).
Humm, Margaret M., Kleinfeld, Erwin
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Completeness of algebraic CPS simulations [PDF]
Electronic Proceedings in Theoretical Computer Science, 2012 The algebraic lambda calculus and the linear algebraic lambda calculus are two extensions of the classical lambda calculus with linear combinations of terms.
Ali Assaf, Simon Perdrix
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On Extensions for Gentle Algebras [PDF]
Canadian Journal of Mathematics, 2020 AbstractWe give a complete description of a basis of the extension spaces between indecomposable string and quasi-simple band modules in the module category of a gentle algebra.
Canakci, Ilke +2 more
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Prime Spectrum of the Ring of Adeles of a Number Field
Mathematics, 2022 Much is known about the adele ring of an algebraic number field from the perspective of harmonic analysis and class field theory. However, its ring-theoretical aspects are often ignored.
Álvaro Serrano Holgado
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Omitting Types in Fragments and Extensions of First Order Logic
Bulletin of the Section of Logic, 2021 Fix \(2 < n < \omega\). Let \(L_n\) denote first order logic restricted to the first n variables. Using the machinery of algebraic logic, positive and negative results on omitting types are obtained for \(L_n\) and for infinitary variants and extensions ...
Tarek Sayed Ahmed
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