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On intra-regular ordered T-semigroups

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2017

Key Words:

Author NameUniversity of Author

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Abstract (2. Language): 
We use the defnition of intra-regularity (left regularity) of po-f-semigroups introduced in 2016 in Armenian Journal of Mathematics. Being able to describe the form of the elements of the principal flter by using this defnition, we study the decomposition of an intra-regular po- f-semigroup into simple components. Then we prove that a po-f-semigroup M is intra-regular and the ideals of M form a chain if and only if M is a chain of simple semigroups. Moreover, a po-f-semigroup M is intra-regular and the ideals of M form a chain if and only if the ideals of M are prime. Finally, for an intra-regular po-f-semigroup M, the set f(x)N j x 2 Mg coincides with the set of all maximal simple subsemigroups of M. A decomposition of some left regular po-f-semigroups into their left simple components is also given.
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REFERENCES

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