The Jacobson radical of a band ring
1989 ◽
Vol 105
(2)
◽
pp. 277-283
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Keyword(s):
A band is a semigroup in which every element is idempotent. In this note we give an explicit description of the Jacobson radical of the semigroup ring of a band over a ring with unity. It is shown, further, that this radical is nil if and only if the Jacobson radical of the coefficient ring is nil. For the particular case of a normal band (see below for the definition) the Jacobson radical of the band ring is nilpotent if and only if the Jacobson radical of the coefficient ring is nilpotent; but this result does not extend to arbitrary bands.
1995 ◽
Vol 37
(2)
◽
pp. 205-210
◽
Keyword(s):
1994 ◽
Vol 49
(1)
◽
pp. 165-170
◽
1976 ◽
Vol 10
(5)
◽
pp. 899-911
◽
1973 ◽
Vol 16
(4)
◽
pp. 551-555
◽
Keyword(s):
1994 ◽
Vol 115
(1)
◽
pp. 27-38
◽
2008 ◽
Vol 2008
◽
pp. 1-6