Annals of Communications in Mathematics

AbstractTo interact somebody with someone various almost ideals (shortly A -ideals), quasi A -ideals, bi quasi A -ideals, tri A -ideals and tri quasi A -ideals in ternary semiring and give some characterizations. We develop the implications ideal =⇒ quasi ideal =⇒ two sided bi quasi ideal =⇒ two sided tri quasi ideal =⇒ two sided tri quasi A -ideal =⇒ two sided bi quasi A -ideal =⇒ bi A -ideal =⇒ quasi A -ideal =⇒ A -ideal and reverse implications do not holds with examples. We show that the union of A -ideals (bi A -ideals, quasi A -ideals, bi quasi A -ideals) is a A -ideal (bi A -ideal, quasi A -ideal, bi quasi A -ideal) in ternary semiring.

AbstractIn this paper, we study various almost ideals (shortly A -ideals), quasi A – ideals, bi quasi A -ideals, tri A -ideals and tri quasi A -ideals in semiring and give some characterizations. Some relevant counter examples are also indicated. We develop the implications ideal =⇒ quasi ideal =⇒ bi quasi ideal =⇒ tri quasi ideal =⇒ tri quasi A -ideal =⇒ bi quasi A -ideal =⇒ bi A -ideal =⇒ quasi A -ideal =⇒ A -ideal and reverse implications do not holds with examples. We show that the union of A -ideals (bi A -ideals, quasi A -ideals, bi quasi A -ideals) is a A -ideal (bi A -ideal, quasi A -ideal, bi quasi A -ideal) in semiring.