Non-Numeric Roots of Pseudo-Algebraic Equations (SEUA Ph.D.)

Original Ph.D. dissertation in Algebra and Number Theory by Loran Jacobs, defended at the State Engineering University of Armenia (Yerevan) in 2008. Delivered as a private page in your member account with permanent access.

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Abstract Edition: the Dissertation Synopsis. The full dissertation is not included.

Defense Edition: the Complete Dissertation, the Dissertation Synopsis and the video of the defense.

Complete Dossier: everything in the Defense Edition, plus the defense presentation, the official reviews and a 20% coupon for a Scientific Advisory session. Academic Provenance: Original Ph.D. dissertation in Algebra and Number Theory (Specialty A.01.06) authored by Loran Jacobs (L.V. Akopyan) and supervised by Prof. V. A. Mirzoyan at the State Engineering University of Armenia (Polytechnic), Yerevan, 2008.

Core Scientific Value: A theoretical framework that extends the notion of a root of an algebraic equation beyond numbers. The work introduces non-numeric (lianit) roots of pseudo-algebraic equations, proves a general theorem linking them to the ordinary numeric roots of polynomials of any degree, and shows how the approach reproduces classical results such as the formulas of Cardano and Ferrari.

Key Research Areas:

• Existence, classification and properties of non-numeric (lianit) roots: primary roots, which uniquely determine a polynomial, and secondary roots, which satisfy innumerable polynomials of the same degree.

• Generalization of Vieta's relations and a reformulation of the Hamilton–Cayley theorem.

• Applications to equations of degrees 3, 4 and 5, elimination of an unknown from systems of nonlinear equations, and raising lianits, including square matrices, to a power.

• Lianit roots of the circle division equation.

Format & Volume: Complete 87-page original academic manuscript. How access works: after payment you receive an email with a link. Sign in with the email address used for your purchase to open your private page. Your access does not expire.