Abstract
Let [Formula: see text] be a non-commutative semiring with [Formula: see text]. We study the notions of 2-absorbing and strong 2-absorbing ideals of [Formula: see text] and we show that if the semiring is commutative, then these two notions are the same. Also, we give an example to show that in general, these two notions are different. Many properties of (strong) 2-absorbing ideals are proved as a generalization to the results for those over rings. For example, we show that a proper subtractive ideal [Formula: see text] of a semiring [Formula: see text] is a 2-absorbing ideal of [Formula: see text] if and only if whenever [Formula: see text], [Formula: see text] and [Formula: see text] are left ideals of [Formula: see text] such that [Formula: see text], then [Formula: see text] or [Formula: see text] or [Formula: see text].
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
