L-fuzzy ideals and L-fuzzy subalgebras of Novikov algebras

Abstract

In this paper, we apply the concept of fuzzy sets to Novikov algebras, and introduce the concepts of L-fuzzy ideals and L-fuzzy subalgebras. We get a sufficient and neccessary condition such that an L-fuzzy subspace is an L-fuzzy ideal. Moreover, we show that the quotient algebra A/μ of the L-fuzzy ideal μ is isomorphic to the algebra A/Aμ of the non-fuzzy ideal Aμ. Finally, we discuss the algebraic properties of surjective homomorphic image and preimage of an L-fuzzy ideal.

Keywords

• fuzzy set
• fuzzy algebra
• fuzzy subalgebra
• fuzzy ideal
• 03e72
• 08a72