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Dec 27, 2020 at 13:50 comment added David Pokorny This answer is accepted in lieu of the answer to the original question, which is in the negative for both; the current version of this question is not the original question but rather a draft of a potential future question. In answer to your question, I don't know about the commutative case.
Dec 27, 2020 at 13:46 vote accept David Pokorny
Dec 27, 2020 at 3:22 comment added Benjamin Steinberg Here I need the number of generators to be at least one to get injectivity of $a\mapsto f_a$.
Dec 27, 2020 at 2:04 comment added Benjamin Steinberg I don't really see how to generalize this. Do you know if your conjecture works for free commutative monoids?
Dec 27, 2020 at 1:13 review Suggested edits
Dec 27, 2020 at 20:37
Dec 26, 2020 at 23:51 comment added David Pokorny Looks good. Two questions occur to me: Can it be generalized? Does it appear in literature?
Dec 26, 2020 at 23:00 history edited Benjamin Steinberg CC BY-SA 4.0
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Dec 26, 2020 at 22:58 history undeleted Benjamin Steinberg
Dec 26, 2020 at 22:56 history deleted Benjamin Steinberg via Vote
Dec 26, 2020 at 22:55 history undeleted Benjamin Steinberg
Dec 26, 2020 at 22:55 history deleted Benjamin Steinberg via Vote
Dec 26, 2020 at 22:53 history undeleted Benjamin Steinberg
Dec 26, 2020 at 22:53 history edited Benjamin Steinberg CC BY-SA 4.0
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Dec 26, 2020 at 22:51 history deleted Benjamin Steinberg via Vote
S Dec 26, 2020 at 22:06 history suggested David Pokorny CC BY-SA 4.0
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Dec 26, 2020 at 22:05 review Suggested edits
S Dec 26, 2020 at 22:06
Dec 26, 2020 at 22:02 history answered Benjamin Steinberg CC BY-SA 4.0