One question related to an ideal of Ring R

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SUMMARY

The discussion focuses on proving that the set { x ∈ R | ax ∈ bR } is an ideal in a commutative ring R, where a and b are elements of R. The proof relies on the definition of an ideal, specifically demonstrating that the set is closed under addition and multiplication by elements of R. Participants emphasize the importance of understanding the ideal properties to complete the proof effectively.

PREREQUISITES
  • Understanding of commutative rings and their properties
  • Familiarity with the definition of an ideal in ring theory
  • Basic knowledge of set notation and operations
  • Experience with algebraic structures and their axioms
NEXT STEPS
  • Study the definition and properties of ideals in ring theory
  • Learn about examples of ideals in specific commutative rings
  • Explore the concept of generated ideals and their significance
  • Investigate the role of homomorphisms in ring theory
USEFUL FOR

Students of abstract algebra, mathematicians focusing on ring theory, and anyone interested in the properties of ideals within commutative rings.

wowolala
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Let a and b belong to a commutative ring R. Prove that { x ∈ R | ax∈bR } is an ideal.

i really need help

thx
 
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just use the definition of an ideal, where are you stuck exactly
 

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