Abstract The concept of $L$-fuzzy ideals of semirings is first introduced in this paper. Based on this new concept, some properties of the category of $L$-fuzzy ideal of semirings are investigated, the result that the category of $L$-fuzzy ideals of semirings is a topological construct on the category of semirings is also proved. Meanwhile, the equalizer, pullback and product are all discussed. On the other hand, the notion of inverse systems of category of $L$-fuzzy ideals of semirings is proposed and the inverse limit of the category of $L$-fuzzy ideals of semirings is constructed. Particularly, the limit mapping has been obtained by means of presenting the mapping between two inverse systems.
Received: 04 January 2017
Published: 07 April 2018
