Julian,W., Mines, R., Richman, F.: Algebraic Numbers, a Constructive Development, Pacific Journal of Mathematics, 74 (1978), 91 -- 102.
Mines, R., Richman, F., Ruitenburg, W.: A Course in Constructive Algebra, Springer, 1988.
Richman, F.: The constructive theory of countable abelian p-groups, Pac. J. Math. 45(1973), 621 - 637.
Richman, F.: Constructive aspects of Noetherian rings, Proc. Amer. Math. Soc. 44(1974), 436 - 441.
Richman, F.: A constructive modification of Vietoris homology, Fundamenta Mathematicae 91(1976), 231 - 240.
Seidenberg, A.: Constructions in Algebra, Trans. Amer. Math. Soc. 197(1974), 273-313.
Stoltenberg-Hansen, V., Tucker, J.V. Computable rings and fields, in: E.R.Griffor (ed.), Handbook of Recursion Theory, to appear.