Module structures and filters on semihoops

In this paper, we study modules and filters on semihoops. Firstly, we introduce the definition of modules on semihoops and give some examples to illustrate it. Also, we get some significant results related to modules on semihoops. If the semihoop G can generate an Abelian group, then G is a module of any subalgebra S of the semihoop G. Then, we use modules and filters to investigate the relationship between modules and semihoops regarding quotient algebras. Secondly, by introducing the definitions of prime submodules and torsion free modules on semihoops, we explore the relationship among prime modules, filters, and torsion free modules. Moreover, we discuss the relationship between the images and inverse images under the homomorphism of semihoops and modules, respectively. Finally, we define multiplication modules and comultiplication modules on semihoops. We study the relationship among multiplication modules and submodules on semihoops and provide the condition for comultiplication modules to satisfy the descending chain condition.

کلیدواژه ها:

semihoop ، Filter ، (prime) module ، torsion free module ، (co)multiplication module