What cause too many math alphabets Issue?

When I try to submit my paper to arXiv, I meet the too many math alphabets Issue. What cause it?

According to this answer^[1], this is because I used the bm package, which double the number of math alphabets while there is a sixteen math alphabets limit for Legacy LaTeX.

To solve the issue, I need to avoid use bm package. Indeed, it is better to redefine each math alphabet to cover Latin and Greek in both bold and regular weights.

Are tensor products of injective modules always injective?

There is a question^[1] on Math.Stackexchange asking this. Under it, a post provides two refrences for general criteria:

• Ishikawa, Takeshi. “On injective modules and flat modules.” Journal of the Mathematical Society of Japan 17.3 (1965): 291-296.
• Enochs, Edgar E., and Overtoun MG Jenda. “Tensor and torsion products of injective modules.” Journal of Pure and Applied Algebra 76.2 (1991): 143-149.

Here I give an example:

$$R=K[x,y]/(x^2,xy,y^2), M=(x,y).$$

In this post, we simplily discuss the basic notions of profinite groups.

This time, we consider another kind of Galois correspondence: the one for covering spaces. This is actually somehow trivial.

This time, we consider a more general case: we give the Galois correspondence for schemes over a field.

In this short post, we point out that the notion of connectedness of schemes is previously a special case of connected objects.

In this post, we discuss the fundamental theorem of Galois theory along the consideration of Galois connections.

I’m a graduated student from Nankai University. My main interesting is in category theory, algebraic geometry and number theory. I’ve held a reading group for couple of years and written lots of math notes. This site is planed to put them and post some short essays. It is welcome for anyone to point out my mistakes.

Remarks: The name “Gau, Syu” is the old-fashion pinyin of my name 高煦. In standard pinyin, my family name should be written as “Gao” and given name as “Xu”.