Fuzzy Baer Subrings: A Fuzzified Extension of Baer Rings

In classical ring theory, a ring  is classified as a Baer ring if, for any subset  the left (or right) annihilator  is generated by an idempotent element in  This paper introduces the concept of fuzzy Baer subrings, extending the principles of Baer rings to the fuzzy setting by defining a fuzzy subset generated by an element and utilizing fuzzy left and right annihilators. Additionally, we develop the theory of fuzzy Rickart subrings by introducing the concept of fuzzy points, establishing that each fuzzy Baer subring inherently qualifies as a fuzzy Rickart subring. Further contributing to fuzzy algebra, we define fuzzy idempotent subrings, capturing broader generalizations in the fuzzy context. This research bridges classical and fuzzy set theories by adapting Baer rings, Rickart rings, and idempotent rings within the framework of fuzzy algebra.