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Approximaitly Prime Submodules and Some Related Concepts
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In this research note approximately prime submodules is defined as a new generalization of prime submodules of unitary modules over a commutative ring with identity. A proper submodule of an -module is called an approximaitly prime submodule of (for short app-prime submodule), if when ever , where , , implies that either or . So, an ideal of a ring is called app-prime ideal of if is an app-prime submodule of -module . Several basic properties, characterizations and examples of approximaitly prime submodules were given. Furthermore, the definition of approximaitly prime radical of submodules of modules were introduced, and some of it is properties were established.
College of Education for Pure Sciences Ibn Al-Haitham
Title: Approximaitly Prime Submodules and Some Related Concepts
Description:
In this research note approximately prime submodules is defined as a new generalization of prime submodules of unitary modules over a commutative ring with identity.
A proper submodule of an -module is called an approximaitly prime submodule of (for short app-prime submodule), if when ever , where , , implies that either or .
So, an ideal of a ring is called app-prime ideal of if is an app-prime submodule of -module .
Several basic properties, characterizations and examples of approximaitly prime submodules were given.
Furthermore, the definition of approximaitly prime radical of submodules of modules were introduced, and some of it is properties were established.
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