7 papers · 1 filter
Similar submodules of projective modules
Alborz Azarang
We introduce a similarity relation between submodules of a module over a ring , extending the classical notion of similarity for right ideals. Focusing on (faithfully) proje…
Non-commutative rings with infinitely many maximal subrings
Alborz Azarang
We study rings with infinitely (only finitely) many maximal subrings. We prove that if is a maximal left/right ideal of a ring which is not an ideal of , and is the…
Maximal subrings of certain non-commutative rings
Alborz Azarang
The existence of maximal subrings in certain non-commutative rings, especially in rings which are integral over their centers, are investigated. We prove that if a ring is inte…
Maximal subrings of division rings
Alborz Azarang
The structure and the existence of maximal subrings in division rings are investigated. We see that if is a maximal subring of a division ring with center and $N(R)\neq…
Classical ideals theory of maximal subrings in non-commutative rings
Alborz Azarang
Let be a maximal subring of a ring . In this paper we study relation between some important ideals in the ring extension . In fact, we would like to find some…
The conductor ideals of maximal subrings in non-commutative rings
Alborz Azarang
Let be a maximal subring of a ring , and , and denote the greatest ideal, left ideal and right ideal of which are contained in , respective…