Definition talk:Unital Algebra

My suggestion is to define a unital algebra as one whose module and multiplication are unitary, and invent 2 new adjectives like pre-unital for algebras whose module or multiplication is unitary.

Why? Because it is convenient to reserve the simplest name for the most often used concept. --barto (talk) 10:04, 21 October 2017 (EDT)


 * I suggest pre-unital for those with a unital module and pseudo-unital for those with a unital multiplication.
 * This is because the unitality of the module can be considered as more primitive/fundamental (hence "pre"), and an algebra with unital multiplication only is like one for which we've forgotten to require that its module must be unital, hence "pseudo-unital". (Acts like a unital algebra, but isn't.)
 * I welcome other ideas. --barto (talk) 10:49, 21 October 2017 (EDT)


 * nope "psuedo" is a bad idea, it's used in Gundogan, Classification and Structure Theory of Lie Algebras of Smooth Sections for something else, and in other papers for yet something else. --barto (talk) 11:11, 21 October 2017 (EDT)
 * It's probably safest to not define them then, for now. --barto (talk) 11:13, 21 October 2017 (EDT)

I went through 20-some books on abstract algebra and did not find an answer. Yay, ProofWiki can take the lead once more. --barto (talk) 10:37, 21 October 2017 (EDT)