Research On Some Problems Of L-fuzzy Subrings And L-fuzzy Subfields

In this paper,we mainly study the related contents of L-fuzzy subrings and L- fuzzy subfields in fuzzy algebra.This paper discusses the relationship between L-fuzzy left(right)-congruence relation and L- fuzzy subring,the relationship between L-fuzzy ring left(right)-congruence relation and L-fuzzy left(right)-ideal,the relationship between L-fuzzy ring congruence relation and L-fuzzy ideal,and the relation between L-fuzzy mod-ule congruence relation and L-fuzzy submodule.The definition of L-fuzzy subfield de-gree and the equivalent characterization of L-fuzzy subfield degree are given,and the relation between L-fuzzy subfield degree and L- fuzzy convex structure and the related properties of these concepts are discussed.In this paper,L is completely distributed.In the first part,we discuss the relationship between L-fuzzy left(right)-congruence relation and L-fuzzy subring on the basis of the definitions of L-fuzzy subring,L-fuzzy left(right)-ideal,etc.It is given and proved that a corresponding L-fuzzy subring can be constructed on the ring.On the contrary,according to a given L- fuzzy left(right)-congruence relation,a L-fuzzy subring can be constructed.It is further proved that there is a one-to-one correspondence between the L- fuzzy left(right)-congruence relation on the ring and the L-fuzzy subring.In the same way,it is proved that L- fuzzy ring congruence relation and L-fuzzy ideal on rings and L-fuzzy module congruence relation and L-fuzzy submodule on modules have corresponding relations.In the second part,a novel approach to the fuzzification of field is introduced,gives the definition of L-fuzzy subfield degree,and gives the equivalent characterization of L-fuzzy subfield degree.It is proposed and proved that an L-fuzzy convex structure can be induced by an L-fuzzy subfield degree,and an L-fuzzy field homomorphism happens to be an L-fuzzy convexity preserving and an L-fuzzy convex-to-convex mapping.And the representation theorem of L-fuzzy subfield product is studied.