A NEW CHARACTERIZATION OF ABSOLUTELY PO-PURE AND ABSOLUTELY PURE S-POSETS

Document Type : Original Manuscript

Authors

1 Department of Mathematics, Faculty of Sciences, Fasa University, P.O. Box: 74617- 81189, Fasa, Iran.

2 Lamerd Higher Education Center, Lamerd, Iran.

Abstract

In this paper, we investigate po-purity using finitely presented S-posets, and give some equivalent conditions under which an S-poset is absolutely po-pure. We also introduce strongly finitely presented S-posets to characterize absolutely pure S-posets. Similar to the acts, every finitely presented cyclic S-posets is isomorphic to a factor S-poset of a pomonoid S by a finitely generated right congruence on S. Finally, the relationships between regular injectivity and absolute po-purity are considered.

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References

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Journal of Algebraic Systems
Volume 8, Issue 1
September 2020
Pages 27-37

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