Titlebook: Algebra 1; Groups, Rings, Field Ramji Lal Textbook 2017 Springer Nature Singapore Pte Ltd. 2017 Algebra.Number System.Group Theory.Arithmet

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Entity Relationship - Modellierung,This chapter is devoted to the study of rings in relation to their arithmetical properties.

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Number System,This is the first introduction to arithmetic in which we develop number systems (including real number system and complex number system) starting from the Peano’s axiom. We also discuss linear diophantine equation and linear congruences.

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Group Theory,One of the most fundamental concepts in mathematics today is that of a group. This present chapter concerns the basic introduction to groups.

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Fundamental Theorems,This chapter is devoted to some fundamental theorems such as Lagrange Theorem and Isomorphism Theorems. We also discuss the direct decomposition of groups into indecomposable groups.

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Permutation Groups and Classical Groups,The two main sources of groups are the permutation groups and the matrix groups. This chapter is devoted to introduce these groups, and to study some of their fundamental and elementary properties.

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Elementary Theory of Rings and Fields,Ring is an important algebraic structure with two compatible binary operations whose intrinsic presence in almost every discipline of mathematics is frequently noticed. The theory of rings, in the beginning, will be developed on the pattern the theory of groups was developed.

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