Title of article :
ON ( m , n ) (m,n)-CLOSED IDEALS IN AMALGAMATED ALGEBRA
Author/Authors :
Issoual, Mohammed Laboratory of Modeling and Mathematical Structures - Department of Mathematics - Faculty of Science and Technology of Fez - University S.M. Ben Abdellah Fez, Morocco , Mahdou, Najib Laboratory of Modeling and Mathematical Structures - Department of Mathematics - Faculty of Science and Technology of Fez - University S.M. Ben Abdellah Fez, Morocco , Salam Moutui, Moutu Abdou Department of Mathematics - College of Science King Faisal University, Saudi Arabia
Abstract :
Let R be a commutative ring with 1 6= 0 and let m and n be
integers with 1 ≤ n < m. A proper ideal I of R is called an (m, n)-closed ideal
of R if whenever am ∈ I for some a ∈ R implies a
n ∈ I. Let f : A → B be
a ring homomorphism and let J be an ideal of B. This paper investigates the
concept of (m, n)-closed ideals in the amalgamation of A with B along J with
respect f denoted by A ./f J. Namely, Section 2 investigates this notion to
some extensions of ideals of A to A ./f J. Section 3 features the main result,
which examines when each proper ideal of A ./f J is an (m, n)-closed ideal.
This allows us to give necessary and sufficient conditions for the amalgamation
to inherit the radical ideal property with applications on the transfer of von
Neumann regular, π-regular and semisimple properties.
Keywords :
(m,n)-closed ideal , radical ideal , semi- n n-absorbing ideal , amalgamated algebra , von Neumann regular ring , π π-regular ring , semisimple ring
Journal title :
International Electronic Journal of Algebra
