A ring or an idempotent semiring is associative provided that additive endomorphisms are multiplicative.
@article{118573, author = {Tom\'a\v s Kepka}, title = {Semirings whose additive endomorphisms are multiplicative}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {34}, year = {1993}, pages = {213-219}, zbl = {0787.16029}, mrnumber = {1241729}, language = {en}, url = {http://dml.mathdoc.fr/item/118573} }
Kepka, Tomáš. Semirings whose additive endomorphisms are multiplicative. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 213-219. http://gdmltest.u-ga.fr/item/118573/
Rings whose additive endomorphisms are ring endomorphisms, Bull. Austral. Math. Soc. 42 (1990), 145-152. (1990) | MR 1066370 | Zbl 0703.16006
Rings in which additive mappings are multiplicative, Studia Sci. Math. Hungar. 22 (1987), 357-359. (1987) | MR 0932222 | Zbl 0647.16028
Rings whose additive mappings are multiplicative, Periodica Math. Hungar. 23 (1991), 65-73. (1991)
Rings whose additive endomorphisms are multiplicative, Periodica Math. Hungar. 19 (1988), 257-260. (1988) | MR 0984775 | Zbl 0671.16016
Additive group of rings, Vol. II, Pitman Research Notes in Math., Series 169, Longman Scient. & Techn., New York, 1988. | MR 0940015
On rings whose additive endomorphisms are multiplicative, Periodica Math. Hungar. 23 (1991), 87-89. (1991) | MR 1141355 | Zbl 0754.16002
Distributive groupoids, Rozpravy ČSAV 91/3 (1981). (1981) | MR 0672563
On a class of non-associative rings, Comment. Math. Univ. Carolinae 18 (1977), 265-279. (1977) | MR 0460393 | Zbl 0366.17016
Additive endomorphisms of rings, Periodica Math. Hungar. 12 (1981), 241-242. (1981) | MR 0642635 | Zbl 0451.16014
Research problem no. 23, Periodica Math. Hungar. 8 (1977), 313-314. (1977) | Zbl 0376.16034