(New page: Q: The ring {0, 2, 4 , 6, 8] under addition and multiplication modulo 10 has a unity. Find it. A: By definition we know that the unity of a ring is a nonzero element that is an identity u...) |
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So we can test each element of the ring {0, 2, 4 , 6, 8] to see which element satisfies these conditions. | So we can test each element of the ring {0, 2, 4 , 6, 8] to see which element satisfies these conditions. | ||
| − | 2*2 = 4 4 modulo 10 = 4 \ | + | 2*2 = 4 4 modulo 10 = 4\neq2 |
Revision as of 04:34, 2 December 2012
Q: The ring {0, 2, 4 , 6, 8] under addition and multiplication modulo 10 has a unity. Find it.
A: By definition we know that the unity of a ring is a nonzero element that is an identity under multiplication (of the ring).
So we can test each element of the ring {0, 2, 4 , 6, 8] to see which element satisfies these conditions.
2*2 = 4 4 modulo 10 = 4\neq2
