Geodesic
A Construction in General Radical Theory
Canadian journal of mathematics, Tome 22 (1970) no. 6, pp. 1097-1100

Voir la notice de l'article provenant de la source Cambridge University Press

Given an arbitrary associative ring R we consider the ring R[x] of polynomials over R in the commutative indeterminate x. For each radical property S we define the function S * which assigns to each ring R the ideal of R. It is shown that the property SA (that a ring R be equal to S *(R)) is a radical property. If S is semiprime, then SA is semiprime also. If S is a special radical, then SA is a special radical. SA is always contained in S. A necessary and sufficient condition that S and SA coincide is given.The results are generalized in the last section to include extensions of R other than R[x], One such extension is the semigroup ring R[A], where A is a semigroup with an identity adjoined. 
Ortiz, Augusto H. A Construction in General Radical Theory. Canadian journal of mathematics, Tome 22 (1970) no. 6, pp. 1097-1100. doi: 10.4153/CJM-1970-126-x
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