Minimal ideals of Abel-Grassmann's groupoids

Khan Waqar; Yousafzai Faisal; Shum Kar-Ping

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2020-06-10 16:43

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KHAN, Waqar, YOUSAFZAI, Faisal, SHUM, Kar-Ping. Minimal ideals of Abel-Grassmann's groupoids. In: Quasigroups and Related Systems, 2016, vol. 24, nr. 1(35), pp. 33-42. ISSN 1561-2848.

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Quasigroups and Related Systems

Volumul 24, Numărul 1(35) / 2016 / ISSN 1561-2848

Minimal ideals of Abel-Grassmann's groupoids

CZU: 512.5

Pag. 33-42

Khan Waqar¹, Yousafzai Faisal¹, Shum Kar-Ping²

¹ University of Science and Technology of China,
² Institute of Mathematics, Yunnan University, Kunming

Disponibil în IBN: 3 august 2016

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We study minimal (0-minimal) ideals, simple (0-simple) Abel-Grassmann's groupoids and zeroids of an Abel-Grassmann's groupoid S. We consider S containing a minimal ideal which is the union of all minimal left ideals of S. The completely simple Abel-Grassmann's groupoid which is equal to the union of all its nonzero minimal left ideals is investigated. In addition, we discuss a universally minimal left ideal of S which is a right ideal and is the kernel of S: Finally, we prove that S contains a left zeroid if and only if it contains a universally minimal left ideal.

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