Can anyone please give some examples or give a reference where I can find examples of non-commutative rings with no multiplicative identity other than matrix rings ? Also examples of finite non-commutative rings and finite rings with no multiplicative identity ?
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the following two links might be helpful: (1)http://math.stackexchange.com/questions/603881/example-of-a-finite-non-commutative-ring-without-a-unity (2)http://math.stackexchange.com/questions/406423/simple-examples-on-non-commutative-rings – Krish Jan 09 '15 at 15:47
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Group algebras for nonabelian groups are noncommutative.
A semi group without identity would create a semigroup algebra without identity.
If the field and the semi group are finite, so I'd the semigroup ring.
rschwieb
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