REGULAR INCLINE AND FIELD SEMIRING
Marapureddy Murali Krishna Rao, B. Venkateswarlu · 2015
We introduce the notion of incline as a generalization of incline, which is an algebraic structure with an additional poset struc- ture. We introduce the notions of regular incline, integral incline, eld incline, eld semiring, simple semiring and pre-integral semiring. We study their properties and relations between them. We prove that if M is a linearly ordered regular incline, then M is a com- mutative incline and M is a eld semiring with an additional prop- erty if and only if M is an integral, simple and commutative semiring. AMS Mathematics Subject Classication (2010): 06F25, 16A09 eld incline; eld semiring; simple semiring