A note on power invariant rings. (1981)

• Record Type: Journal Article
• Authors: Kim, Joong Ho
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 4:Number 3(1981)
• Page Start: 485
• Page End: 491
• Publication Date: 1981
• Subjects: power series ring -- power invariant ring -- forever-power-invariant -- ideal-adic topology; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171281000343
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : LetR be a commutative ring with identity andR ( ( n ) ) = R [ [ X 1, …, X n ] ] the power series ring inn independent indeterminatesX 1, …, X n overR .R is called power invariant if wheneverS is a ring such thatR [ [ X 1 ] ] ≅ S [ [ X 1 ] ], thenR ≅ S .R is said to be forever-power-invariant ifS is a ring andn is any positive integer such thatR ( ( n ) ) ≅ S ( ( n ) ) thenR ≅ S LetI C ( R ) denote the set of alla ∈ R such that there isR - homomorphismσ : R [ [ X ] ] → R withσ ( X ) = a . ThenI C ( R ) is an ideal ofR . It is shown that ifI C ( R ) is nil, R is forever-power-invariant