TY - JOUR
T1 - Matrix rings of finite degree of nilpotency
AU - Klein, Abraham A.
PY - 1971/2
Y1 - 1971/2
N2 - The degree of nilpotency of a ring R is defined to be the supremum of the orders of nilpotency of its nilpotent elements and it is denoted by v(R). We consider the degree of nilpotency of the ring of m x m matrices Rm over a ring R. We obtain given results concerning the degrees v(Rm) for distinct m’s, in the case R has no nonzero two-sided annihilators. It is shown that if v(Rm) = m for some m, and if R' is a ring containing R as an ideal such that R' has no nonzero two-sided annihilators of R, then (FORMULA PRESENTED). An application of this result is given.
AB - The degree of nilpotency of a ring R is defined to be the supremum of the orders of nilpotency of its nilpotent elements and it is denoted by v(R). We consider the degree of nilpotency of the ring of m x m matrices Rm over a ring R. We obtain given results concerning the degrees v(Rm) for distinct m’s, in the case R has no nonzero two-sided annihilators. It is shown that if v(Rm) = m for some m, and if R' is a ring containing R as an ideal such that R' has no nonzero two-sided annihilators of R, then (FORMULA PRESENTED). An application of this result is given.
UR - http://www.scopus.com/inward/record.url?scp=84972580664&partnerID=8YFLogxK
U2 - 10.2140/pjm.1971.36.387
DO - 10.2140/pjm.1971.36.387
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AN - SCOPUS:84972580664
SN - 0030-8730
VL - 36
SP - 387
EP - 391
JO - Pacific Journal of Mathematics
JF - Pacific Journal of Mathematics
IS - 2
ER -