Recent content by blacklily

Can we construct a perfect crystal? Like constructing a perfect circle.

Hi, I am just wondering is there such thing as perfect crystal. I don't know much about this stuff. It seems to me it's just a theoretical idea, because nothing is really "perfect" in this world. Anyways, I just want to know more about perfect crystal. If they do exist, what is a perfect crystal?

I see. In any case, I am use to the definition of a basic ring without the 1 identity. A ring with 1 is an additional property. I guess your example wouldn't work in my class. Any thoughts on the orginal question?

You don't need to have multiplicative identity, ie 1, for something to be a ring. Or am I wrong? Edit: Thanks for explaining my question, you made it that much easier to understand. haha...

I understand what you are saying and what you said is true. But what I want is: For example: Show (------) is a subring of (______). Students would proceed the subring test using: (1) closed under subtraction (2) closed under multiplication but (------) is actually a empty subset of (______)...

My teacher put heavy emphases on acknowledging that a subset is nonempty of a ring when proving something is a subring of something. For the final exam, she wants to put a question with empty subset of a ring, and do subring proof. The empty subset would have "nice" description so you can do...