On some properties of polynomials rings

Abstract

For a commutative ring with unity R, it is proved that R is a PF-ring if and only if the annihilator, annR(a), for each a ϵ R is a pure ideal in R, Also it is proved that the polynomial ring, R[X], is a PF-ring if and only if R is a PF-ring. Finally, we prove that R is a PP-ring if and only if R[X] is a PP-ring.

Keywords

• polynomial rings
• pure ideal
• PF-ring
• PP-ring
• R-flatness
• and idempotent elements.