Open AccessThe Propositions and Proofs in Algebra System
Author(s) -
Shiqing Chen
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1650/3/032023
Subject(s) - algorithm , computer science
In the study, it was proved that the algebra system ( a + b p , ⊕ , ⊙ ) = { a + b 2 | a , b ∈ Z } is a Ring of integers and not a domain, and when 2 is extended to the prime number, the conclusion is correct. When a and b are Rational number and Real number, it proves that Algebra System ( a + b p , ⊕ , ⊙ ) = { a + b 2 | a , b ∈ Z } is a domain and extends 2 to 5 until p is the prime number. The conclusion is correct. Finally, the judgment method of Subdomains is used to prove that when a and b are plural, I = { a + bi | a , b ∈ Q }is a domain.