On separable extensions of group rings and quaternion rings
1978 ◽
Vol 1
(4)
◽
pp. 433-438
Keyword(s):
The purposes of the present paper are (1) to give a necessary and sufficient condition for the uniqueness of the separable idempotent for a separable group ring extensionRG(Rmay be a non-commutative ring), and (2) to give a full description of the set of separable idempotents for a quaternion ring extensionRQover a ringR, whereQare the usual quaternionsi,j,kand multiplication and addition are defined as quaternion algebras over a field. We shall show thatRGhas a unique separable idempotent if and only ifGis abelian, that there are more than one separable idempotents for a separable quaternion ringRQ, and thatRQis separable if and only if2is invertible inR.
2019 ◽
Vol 11
(2)
◽
pp. 264-270
2019 ◽
Vol 19
(09)
◽
pp. 2050173
2019 ◽
Vol 18
(01)
◽
pp. 1950006
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2015 ◽
Vol 14
(07)
◽
pp. 1550099
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2000 ◽
Vol 23
(4)
◽
pp. 279-283
2011 ◽
Vol 21
(03)
◽
pp. 409-431
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1975 ◽
Vol 12
(3)
◽
pp. 449-456
◽
2017 ◽
Vol E100.A
(12)
◽
pp. 2764-2775
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