摘要
<span style="font-family:Verdana;">Let <img alt="" src="Edit_1798cf4c-b9a5-4ada-b2d4-9fbf535a6d28.png" />be the partial symmetric semigroup on <img alt="" src="Edit_86c31e58-0588-44fc-8ff3-78c73dc14be6.png" />and let <img alt="" src="Edit_09f7ec2a-49d1-463d-952e-93fbe00740cd.png" />and <img alt="" src="Edit_4aca07c1-9a36-44b6-83af-46fdd6278ca4.png" />be its subsemigroups of order-preserving contractions and order-preserving, order-decreasing contractions mappings of <img alt="" src="Edit_72d2bbdf-2b96-4812-a993-f49640bb98c9.png" />, respectively. In this paper we investigate the cardinalities of <img alt="" src="Edit_95038cdc-5496-495f-bfb9-29c817ba2df4.png" />and <img alt="" src="Edit_f8d3d782-ff8c-43b3-84af-d21a3f4291d5.png" />, the set idempotents of <img alt="" src="Edit_ac8237f8-83ec-4767-9029-b546377bf106.png" />and <img alt="" src="Edit_8b1bf8bf-7472-453c-965d-7308da5b4f4c.png" />, respectively. We also investigate the cardinalities of certain equivalences on <img alt="" src="Edit_e5f7aec4-67c1-48ba-8d03-ea6ceb2e7627.png" />and <img alt="" src="Edit_42a31943-fe9d-4ea8-8999-3aadb705fb38.png" />.</span>
<span style="font-family:Verdana;">Let <img alt="" src="Edit_1798cf4c-b9a5-4ada-b2d4-9fbf535a6d28.png" />be the partial symmetric semigroup on <img alt="" src="Edit_86c31e58-0588-44fc-8ff3-78c73dc14be6.png" />and let <img alt="" src="Edit_09f7ec2a-49d1-463d-952e-93fbe00740cd.png" />and <img alt="" src="Edit_4aca07c1-9a36-44b6-83af-46fdd6278ca4.png" />be its subsemigroups of order-preserving contractions and order-preserving, order-decreasing contractions mappings of <img alt="" src="Edit_72d2bbdf-2b96-4812-a993-f49640bb98c9.png" />, respectively. In this paper we investigate the cardinalities of <img alt="" src="Edit_95038cdc-5496-495f-bfb9-29c817ba2df4.png" />and <img alt="" src="Edit_f8d3d782-ff8c-43b3-84af-d21a3f4291d5.png" />, the set idempotents of <img alt="" src="Edit_ac8237f8-83ec-4767-9029-b546377bf106.png" />and <img alt="" src="Edit_8b1bf8bf-7472-453c-965d-7308da5b4f4c.png" />, respectively. We also investigate the cardinalities of certain equivalences on <img alt="" src="Edit_e5f7aec4-67c1-48ba-8d03-ea6ceb2e7627.png" />and <img alt="" src="Edit_42a31943-fe9d-4ea8-8999-3aadb705fb38.png" />.</span>
作者
Oladapo Adekunle Ojo
Fatma Salim Ali Al-Kharousi
Abdullahi Umar
Oladapo Adekunle Ojo;Fatma Salim Ali Al-Kharousi;Abdullahi Umar(Oyo State College of Agriculture and Technology, Igboora, Oyo State, Nigeria;Department of Mathematics, Sultan Qaboos University, Al-Khod, Muscat, Oman;Department of Mathematics, Khalifa University of Science and Technology, Sas Al-Nakhl, Abu Dhabi, U. A. E.)
