Abstract / Excerpt:

Objectives: It is the purpose of this study to propose new notations and identify applications of the general algebraic systems. It answers: (1) What new notation can be proposed to replace the existing old notation of each of the following systems? 1. a) groups, b) abelian groups. 2. a) rings, b) commutative rings, c) commutative rings with unity 3. Integral domains 4. a) fields, b) ordered fields, c) complete ordered fields. (2) What are the applications of the systems, a) related mathematics, b) meachanics, c) electromagnetism?
Methodology: Steps involved in the research methodology include (1) Collection of notations and terms from books in mathematics, physics and electronics, (2) Analyses of the collected notations and applications, (4) Coming up with new notations and applications, (5) Validation of the new notations and applications by the same experts, (6) finalization of new notations and applications, and (7) proposing new notations and application of the general algebraic systems.
Findings: (1) The new notations of the general algebraic systems in this study are as follows: G for a group; AG for an abelian group; R for a ring; CRi for a commulative ring; CRU for a commulative ring the unity; D for integral domain; F for field; OF for an ordered field; and COF for a complete ordered field. (2) The applications of the abstract system in related mathematics are the following: a) the set of 2x2 matrics M and the set of vectors V are abelian groups AG with respect to addition. c) The set of 2x2 matrics M is a ring R with respect to addition and multiplication. d) The set of integers Z is a commutative ring CR and a commutative ring with unity CRU with respect to addition and multiplication. e) Z where p is prime, the set of finite P integers in modulo p is an integral domain D and a field F with respect to addition and multiplication. f) The set if rational numbers Q is an ordered field OF with respect to addition and multiplication. g) The set of real numbers R is a complete ordered field COF with respect to addition and multiplication. (3) The application of the abstract systems in mechanics are the following: a) vector quantities like sets of velocities, accelerations, forces, momentum, torques, and projectiles are abelian groups AG with respect to addition. b) Scalar quantities like sets of displacements of an object moved in a frictionless plane and displacements in the rotations of a wheel are abelian groups AG with respect to addition. c) Gravitational field is an abelian group with respect to addition and multiplication. (4) The application of the abstract systems in electromagnetism are: a) the set of electrolastic forces called electric field is an abeliam group AG with respect to addition. b) the set of magnetic forces called magnetic field is an abelian group AG with respect to addition.

Info

Source Institution	Ateneo de Davao University
Unit	Natural Science
Authors	Daleon, Sixto O.
Page Count	1
Place of Publication	Davao City
Original Publication Date	March 5, 1990
Tags	Dissertations, Mathematics

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