### Biography

Yonghua Xu, Chinese mathematician (Yinxian, Zhejiang Province 01 January 1932 – 2019)

Introduced the concepts of O-ideal and O-homomorphic mapping

On the O-structure of rings (1977)

Put forward the concept of non-associative and non-distributive rings

Non-associative and non-distributive rings. I. Scientia Sinica 22 (2):135-48, 1979

Non-associative and non-distributive rings. II. Acta Math. Sinica 21:300-11, 1978

Non-associative and non-distributive rings. III. Acta Math. Sinica 22(1):1-13, 1979

Derived a theorem concerning the structure of non-associative and non-distribuive rings under the minimal condition

Non-associative and non-distributive rings satisfying the minimal condition for right ideals (1979)

Established the finite structure theorem between complete rings of linear transformations (1979)

A finite structure theorem between primitive rings and its application to Galois theory. Chin. Ann. Math. 1(2):183-97, 1980

A generalized Wolfson’s theorem. Adv. in Math. 13:213-5, 1984

Gave a necessary and sufficient condition for the equivalence of right and left semi-prime Goldie rings and some properties of Goldie rings

A note on semi-prime Goldie rings. Rendic. Circolo Matem. Palermo 36:220-40, 1987

With K.P. Shum & Y. Fong. A decomposition theory of comodules 170(3):880-906, 1994

Introduced the notion of quantum cocommutativity

With G.G. Hu. Quantum commutative algebras and their duals (1997)

Introduced a new concept for direct product rings which generalizes the usual ones

With K.P. Shum. New direct product rings, their structure and applications. Algebra Colloq. 1(4):493-514, 2004