ON SIMPLE LEFT, RIGHT AND TWO-SIDED IDEALS OF AN ORDERED SEMIGROUP HAVING A KERNEL

Title & Authors
ON SIMPLE LEFT, RIGHT AND TWO-SIDED IDEALS OF AN ORDERED SEMIGROUP HAVING A KERNEL
Changphas, Thawhat;

Abstract
The intersection of all two-sided ideals of an ordered semigroup, if it is non-empty, is called the kernel of the ordered semigroup. A left ideal L of an ordered semigroup ($\small{S,{\cdot},{\leq}}$) having a kernel I is said to be simple if I is properly contained in L and for any left ideal L of ($\small{S,{\cdot},{\leq}}$), I is properly contained in L and L is contained in L imply L
Keywords
Language
English
Cited by
References
1.
G. Birkhoff, Lattice Theory, 25, Rhode Island, American Mathematical Society Collo-quium Publ., Am. Math. Soc., Providence, 1984.

2.
N. Kehayopulu, On weakly prime ideals of ordered semigroups, Math. Japon. 35 (1990), no. 6, 1051-1056.

3.
N. Kehayopulu and S. Tsingelis, A note on groupoids-semigroups, Sci. Math. 3 (2000), no. 2, 251-255.

4.
N. Kehayopulu and S. Tsingelis, On kernels of ordered semigroups-a corrigendum, Commun. Korean Math. Soc. 28 (2013), no. 2, 225-229.

5.
M. Petrich, Introduction to Semigroups, Merrill, Columbus, 1973.

6.
St. Schwarz, On semigroups having a kernel, Czechoslovak Math. J. 1(76) (1951), 229-264.