Some new results on regular modules

Laleh Oftadeh, Naser Amiri


The aim of this paper is to study unitary regular modules on commutative rings with identity. Regularity accompanied by cocyclic property results in some prime-related conclusions on both modules and rings. Further to this, regularity addresses also radical property of submodules and they are related closely. This property not only affects the modules on ring $R$ but also restricts R to totally idempotent one.


Regular module; Pure submodule; Prime submodule; Primary submodule; Isolated submodule.

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