Talk:Primitive element (co-algebra)

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If this is really a notion in co-algebras, what is the meaning of 1? Usually, 1 denotes the unit element with respect to a multiplication. So, we need a multiplication on our co-algebra, making this really a notion about bi-algebras rather than co-algebras, right? --130.83.2.27 (talk) 12:21, 6 November 2014 (UTC)[reply]

That's a very good point, but the definition is ok. A co-algebra is still a vector space over a field and the field has the multiplicative identity element 1. -- Taku (talk) 13:47, 6 November 2014 (UTC)[reply]

but Delta(x) is an element in C Tensor C, hence x Tensor 1 should also be in C Tensor C, imlpying that 1 should be in C, hence, this 1 is not The 1 in the field. --80.187.113.79 (talk) 12:05, 7 November 2014 (UTC)[reply]

You're right. One should use a lift of 1 in the base field. The article has been corrected. And thank you for pointing out the error. -- Taku (talk) 16:01, 7 November 2014 (UTC)[reply]