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Turkish Journal of Mathematics

DOI

10.55730/1300-0098.3146

Abstract

This note is written to show that the definition of the ${\cal L}{\cal A}$-semihypergroup by V. Amjad, K. Hila and F. Yousafzai "Generalized hyperideals in locally associative left almost semihypergroups, New York J. Math. 2014" should be corrected and that it is not enough to replace the multiplication "$\cdot$" of an ${\cal L}{\cal A}$-semigroup by the hyperoperation "$\circ$" to pass from an ${\cal L}{\cal A}$-semigroup to an ${\cal L}{\cal A}$-semihypergroup. The two examples of the paper based on the definition of the ${\cal L}{\cal A}$-semihypergroup are wrong that is a further indication that this definition needs correction. According to the last section of the paper, the paper generalizes the results of an ${\cal L}{\cal A}$-semigroup by M. Akram, N. Yaqoob and M. Khan "On $(m,n)$-ideals of left almost semigroups, Appl. Math. Sci. (Ruse) 2013" while the paper duplicates, without citation, the section 4 of the paper by W. Khan, F. Yousafzai, W. Guo and M. Khan "On $(m,n)$-ideals of left almost semigroups, J. Semigroup Theory Appl. 2014" with the usual change of "$\cdot$" to "$\circ$".

Keywords

Left almost semihypergroup, Abel-Grassmann's groupoid

First Page

1113

Last Page

1118

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