Unification Theories: Examples and Applications
Round 1
Reviewer 1 Report
I suggest that the concept of unification (in the author's sense) should
be described in the introduction, so that the readers may have more than
an intuitive impression about it on the basis the the later parts.
Otherwise I find the paper nice but written in a somewhat loose style
(as expressions as e.g. "the main nonassociative structures are Lie
algebras and Jordan algebras" on page 1)
I think the paper can be published with an extended introduction and
after minor stylistical improvements (resulting in an about one page
longer size only).
Author Response
Dear Reviewer,
Thank you very much for your comments.
I have improved the introduction: I have added two paragraphs about unification theories in mathematics and physics in the beginning of the introduction.
I made some other changes: in the beginning of subsection 3.1 and in the last remark. (I also removed a remark from subsection 3.1.)
Thank you again.
Best wishes,
Author
Author Response File: 
Author Response.pdf
Reviewer 2 Report
In this communication, the author comments on two unification problems in mathematics, related to the theory of transcendental numbers and to non-associative algebras. Unification theories, as conceived in physics, have contributed to a better understanding of certain phenomena, and the unified approaches suggested in this note are of interest, as they refer to the theory of functions and algebraic structures, two of the pilar of modern physical tools.
The note is interesting, but requires some amendments prior to its publication.
Page , line 12: Replace ``Hopf algebra theory are``by ``Hopf algebra theory is``
Page 1, line 26: Replace ``transcental``by ``trascendental``
Page 3, line 66: When defining UJLA structures, a sentence commenting on its motivation would be useful to settle the context.
Page 5, line 114: As the proof is not given, it is better to replace the sentence by something like ``The proof follows the same argumentation as the previous one, for which reason it is omitted.``
Page 5, remark 3.13: The assertion is a little ambiguous. It is suggested to indicate that three types of unifications have been considered: structures, categories and theorems. And that it is currently an open problem whether these types can be formulated in unified form.
Page 5, References: The format of the references should be normalized.
Once these minor corrections have been completed, the note is judged suitable for publication.
Author Response
Dear Reviewer,
I would like to thank you for your report. I have extended the introduction.
The corrections on pages 1 and 5 were made according to your suggestions.
I added a motivation for defining UJLA structures (related to Grassmanian manifolds).
Thank you.
Best wishes,
Author
Author Response File: Author Response.pdf
