Revista de la
Unión Matemática Argentina
On classes of finite rings
Aleksandr Tsarev
Volume 61, no. 1 (2020), pp. 103–111

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A class of rings is a formation whenever it contains all homomorphic images of its members and if it is subdirect product closed. In the present paper, it is shown that the lattice of all formations of finite rings is algebraic and modular. Let $R$ be a finite commutative ring with an identity element. It is established that there is a one-to-one correspondence between the set of all invariant fuzzy prime ideals of $R$ and the set of all fuzzy prime ideals of each ring of the formation generated by $R$.