Results 181 to 190 of about 2,863 (231)
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HOPF–GALOIS STRUCTURES ON FIELD EXTENSIONS WITH SIMPLE GALOIS GROUPS
Bulletin of the London Mathematical Society, 2003Let \(L/K\) be a Galois extension of fields with Galois group \(G\). Then the group ring \(KG\) endows \(L/K\) with a Hopf Galois structure. There may be other \(K\)-Hopf algebras \(H\) endowing \(L/K\) with a Hopf Galois structure; all of them are forms of group rings over \(L\).
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Field Theory of Galois' Fields
1995The motivation for the present work comes from various sources which, however, need not be elaborated on here. I will be exploring a class of quantum field theories defined over finite sets of integers. Essentially these are the familiar Z„ lattice theories, but carried to their logical extremes.
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1995
Consider an algebraic system \(\langle SF, +, \cdot \rangle\) consisting of a finite set of elements, \(SF\) with two binary operations, addition and multiplication, \(|SF|=q\), \(q\) an arbitrary integer \(\geq 2\). A spurious Galois field, \(SGF(q)\) satisfies, in addition, the following axioms: A.1.
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Consider an algebraic system \(\langle SF, +, \cdot \rangle\) consisting of a finite set of elements, \(SF\) with two binary operations, addition and multiplication, \(|SF|=q\), \(q\) an arbitrary integer \(\geq 2\). A spurious Galois field, \(SGF(q)\) satisfies, in addition, the following axioms: A.1.
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment
Ca-A Cancer Journal for Clinicians, 2022Jun J Mao,, Msce +2 more
exaly
2017
This chapter is devoted to the theory of fields, Galois theory, geometric constructions by ruler and compass, and the theorem of Abel–Ruffini about the polynomial equations of degree \(n, n\ge 5\). We also discuss cubic and biquadratic equations.
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This chapter is devoted to the theory of fields, Galois theory, geometric constructions by ruler and compass, and the theorem of Abel–Ruffini about the polynomial equations of degree \(n, n\ge 5\). We also discuss cubic and biquadratic equations.
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Radiotheranostics in oncology: Making precision medicine possible
Ca-A Cancer Journal for Clinicians, 2023Eric Aboagye
exaly
1974
The first principal theme of this chapter is the structure theory of fields. We shall study a field F in terms of a specified subfield K (F is said to be an extension field of K). The basic facts about field extensions are developed in Section 1, in particular, the distinction between algebraic and transcendental extensions.
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The first principal theme of this chapter is the structure theory of fields. We shall study a field F in terms of a specified subfield K (F is said to be an extension field of K). The basic facts about field extensions are developed in Section 1, in particular, the distinction between algebraic and transcendental extensions.
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Genetic testing in prostate cancer management: Considerations informing primary care
Ca-A Cancer Journal for Clinicians, 2022Veda N Giri +2 more
exaly