A Class of BCI-Algebra and Quasi-Hyper BCI-Algebra
Round 1
Reviewer 1 Report
Here are my comments on the paper for the authors.abstract lines 3-4: I do not understand the sentence
line 6: is a generalized
p. 1 l. -11: is an Abelian group
l. -8 and -5: hyperstructure
def. 7: I do not understand
thm 3: I do not understand
prop. 2: what is the BCK part?
def. 10: define the << symbol before def. 10
section 3 before theorem 5: the symbol * has two meanings?
thm 5 I do not understand the statement, in particular I do not understand what M(X) is.
page 4 last line: The operation * is defined in table 1
proof of theorem 5: separate the four cases more clearly
def. 13: containing
theorem 8: I do not understand the statement
theorem 9: what is the difference with theorem 5?
def. 15 I do not understand
def. 16: containing
p. 13 l. -12: they show
p. 14 l. 10: the following holds
l. -9: idem
def. 19: for all x in H we have...
p. 16 l. -13: hyperstructure
example 6: I do not understand, maybe you mean that your example satisfies the hypotheses of theorem 17.
page 17 l. 14: operation
table 10: is it correct?
example 7: again, maybe you mean that your example satisfies the hypotheses of theorem 18
table 12: is it correct?
def. 21: I do not understand
pag. 20 l. 2-3: I do not understand
Summing up, I recommend major revision because many points are not clear.
Author Response
Dear Professor:
Thank you for your letter and for the reviewers’ comments concerning our manuscript. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval.
The main corrections in the paper and the responds to the reviewer’s comments are in PDF
All the best!
Xiaohong Zhang; Yudan Du
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Definition 1: regelar -> regular
While the manuscript accomplishes exactly the goal it sets out to do, it would be more pleasant to have some introductory text to each section.
Author Response
Dear Professor:
Thank you for your letter and for the reviewers’ comments concerning our manuscript. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. The main corrections in the paper and the responds to the reviewer’s comments are as follows:
- I'm very sorry for some spelling error about ‘regular’, and have corrected them.
- According to your advice, we have added some introductory text in each section.
Added “Firstly, we introduce the adjoint semigroup of BCI-algebra and give some examples about adjoint semigroup of BCI-algebra. Then we discuss the relationshipn between adjoint semigroup of generalized quasi left alter BCI-algebra and commutative Clifford semigroup.” at the beginning of Section 3.
Added “Above all, we prove that generalized quasi left alter BCI-algebra, QM-BCI algebra and generaized quasi left alter hyper BCI-algebra are equivalent to one another. And they are QM-hyper BCI-algebra. ” at the end of Section 3.
Added “At the beginning of this part, we introduce the definition of quasi-hyper BCI-algebras.” at the beginning of Section 4.
All the best!
Xiaohong Zhang; Yudan Du
Round 2
Reviewer 1 Report
Here are some typos and minor points:
p. 3/8: what is P*(H)?
p. 4 before theorem 5: the double use of * is confusing?
theorem 5: I do not understand the statement and in particular I do not understand what is M(X), it should be
defined clearly and separately
theorem 8: why K(X) and not B(X)? and what is AG(X)?
theorem 9: again I do not understand
p. 14/-6: define more clearly Hv-groups
theorem 15: I do not understand
reference 35: hyperstructures
The paper can be accepted provided the definitions are given more clearly. So I recommend a minor revision.
Author Response
Dear Professor:
Thank you for your letter and for the reviewers’ comments concerning our manuscript. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. The main corrections in the paper and the responds to the reviewer’s comments are in PDF.
All the best!
Xiaohong Zhang; Yudan Du
Author Response File: Author Response.pdf
