Generalized anti-commutative Grobner-Shirshov basis theory and free Sabinin algebras

摘要

E. Chibrikov defined regular monomials (here called Chibrikov words) and proved that they form a linear basis of a free Sabinin algebra. In this paper, we introduce the notion of a generalized anti-commutative algebra and establish Grobner-Shirshov basis theory for those algebras. We provide another approach to the definition of Chibrikov words i.e. we find a generalized anti-commutative Grobner-ShirshovSof a free Sabinin algebra such thatIrr(S) is the set of all Chibrikov words onX, whereIrr(S) is the set of all normal omega-words not containing maximal monomials of polynomials fromS. Following from Grobner-Shirshov basis theory of generalized anti-commutative algebras, the setIrr(S) is a linear basis of a free Sabinin algebra.