Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
6. Algebra and the arithmetic of remainders
View through CrossRef
‘Algebra and the arithmetic of remainders’ considers a new type of algebra, which is both an ancient topic and one that has found major contemporary application in Internet cryptography. It begins with an outline of abstract algebra, including groups, rings, and fields. Semigroups and groups are algebras with a single associative operation, while rings and fields are algebras with two operations linked via the distributive law. Lattices are algebras with an ordered structure, while vector spaces and modules are algebras where the members can be multiplied by scalar quantities from other fields or rings. The rules of modular arithmetic (or clock arithmetic) and solving linear congruences are also described.
Title: 6. Algebra and the arithmetic of remainders
Description:
‘Algebra and the arithmetic of remainders’ considers a new type of algebra, which is both an ancient topic and one that has found major contemporary application in Internet cryptography.
It begins with an outline of abstract algebra, including groups, rings, and fields.
Semigroups and groups are algebras with a single associative operation, while rings and fields are algebras with two operations linked via the distributive law.
Lattices are algebras with an ordered structure, while vector spaces and modules are algebras where the members can be multiplied by scalar quantities from other fields or rings.
The rules of modular arithmetic (or clock arithmetic) and solving linear congruences are also described.
Related Results
Domain kognitif dan pencapaian ungkapan algebra dalam kalangan pelajar Tingkatan Dua
Domain kognitif dan pencapaian ungkapan algebra dalam kalangan pelajar Tingkatan Dua
Algebra merupakan salah satu topik yang sukar dalam pembelajaran Matematik khususnya di peringkat Menengah Rendah. Permasalahan pelajar dalam topik Algebra sering dikaitkan dengan ...
Do Reading and Arithmetic Fluency Share the Same Cognitive Base?
Do Reading and Arithmetic Fluency Share the Same Cognitive Base?
We examined the role of different cognitive-linguistic skills in reading and arithmetic fluency, and whether the effects of these skills are mediated by reading and arithmetic accu...
The Weil Algebra and the Weil Model
The Weil Algebra and the Weil Model
This chapter evaluates the Weil algebra and the Weil model. The Weil algebra of a Lie algebra g is a g-differential graded algebra that in a definite sense models the total space E...
Quasi-pre-Lie bialgebras and twisting of pre-Lie algebras
Quasi-pre-Lie bialgebras and twisting of pre-Lie algebras
Given a (quasi-)twilled pre-Lie algebra, we first construct a differential graded Lie algebra ([Formula: see text]-algebra). Then we study the twisting theory of (quasi-)twilled pr...
Lukasiewicz Fuzzy BM-Algebra and BM-Ideal
Lukasiewicz Fuzzy BM-Algebra and BM-Ideal
Introduction: ℱ???????????????? Sets is a mathematical framework that expands the traditional concept of sets by enabling elements to have degrees of membership. This enables parti...
Algebra on demand
Algebra on demand
School districts nationwide have yet to agree upon a standardized method for student achievement in algebra at the middle school level. This comparative case study, with a phenomen...
The Remainder
The Remainder
AbstractThis chapter suggests that we should question whether private law is genuinely about legal wrongs. It argues that the correction of wrongs ordinarily leaves a normative rem...
Remainders
Remainders
Remainders: American Poetry at Nature’s End discusses postwar poetry as an essential archive of ecological thinking in the era of the Great Acceleration, a period of rapid and unpr...