PSEUDO INTEGRAL TERNARY SEMIGROUPS

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D. Madhusudhana Rao, Y. S. A. (2013). PSEUDO INTEGRAL TERNARY SEMIGROUPS. Asian Journal of Current Engineering and Maths, 2(1). Retrieved from http://innovativejournal.in/index.php/ajcem/article/view/144
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Abstract

n this paper, the term, ‘pseudo integral ternary semigroup’ is introduced.  It is proved that every pseudo symmetric ternary semigroup with nonempty kernel is a pseudo integral ternary semigroup.  It is also proved that an ideal a of a ternary semigroup t is pseudo symmetric iff t\a is a pseudo integral ternary semigroup.  If t is a pseudo integral ternary semigroup then it is proved that t is strongly archimedean, t is archimedean, t has no proper completely prime ideals, t has no proper completely semiprime ideals, t has no proper prime ideals, t has no proper semiprime ideals, every element in t is a k-potent element are equivalent.  It is proved that if s is a maximal ternary subsemigroup of a pseudo integral ternary semigroup t such that  then t\s is a minimal prime ideal in t.

 

Mathematical  subject classification (2010) : 20M07; 20M11; 20M12.

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