The First Isomorphism Theorem on QI-algebras

Sassanapitax, Lee

doi:10.24203/ajas.v8i3.6186

Cited by 1 publication

(1 citation statement)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A homomorphism is mapping one mathematical set to another set or to itself in such a way that the result obtained from an operation on the elements of one group is mapped to the result obtained from a corresponding operation on the related images in the other set. In abstract algebra, isomorphism is a bijection in the structure that doesn't change [3]. In general category theory, isomorphism involves the existence of a state projection and another state projection such that the composite of the two is a constant state projection [4].…”

Section: Introductionmentioning

confidence: 99%

Homomorphism, Isomorphism, and Their Applications in Group Theory

Cheng¹

2023

HSET

View full text Add to dashboard Cite

The main study of modern algebra is the so-called algebraic systems, i.e., sets with operations. Modern algebra has important applications in other branches of mathematics and natural science. In modern algebra, homomorphism and isomorphism are relatively elementary but extremely important concepts that are interrelated and different. A homomorphism is a mapping that preserves the constitution of a mathematical format and is a generalization of a homomorphism. it is a structurally invariant mapping between two algebraic structures in abstract algebra. The conditions for a homomorphism to be a homomorphism in different algebraic systems are different, and the conditions for a homomorphism to be a homomorphism are described here. Some applications of homomorphisms and homomorphisms to different algebraic systems are discussed, from which the importance of homomorphisms and homomorphisms is illustrated.

show abstract

Section: Introductionmentioning

confidence: 99%