The site is installed Article Sharing and Artio Joomsef, all materials published on the site of the main page of the subdomain. Blog categories that I have created through Article Sharing a URL is:
domen.ru/category_name/category/blog/master-db/1.html
the material has an URL
domen.ru/category_name/article/389-2013-05-26-21-22-45/1-2011-07-24-14-49-29/master-db.html
How do I make reference to a category was identical as the main site, ie:
domen.ru/category_name /blog.html
a link to the material looked like this:
domen.ru/category_name/article_name.html
What should I do?

First, the SEF path is the one generated by Joomla and is correct.

As you are using a specific SEF extension, you can setup the artio to replace this default SEF value by another one.

Another possibility when there is no specific SEF extension is to create a specific hiddent menu item that point directly to this page. In this case, this will be the menu item alias that will be used to match this article.
So you could have domain.ru/mysef_article.html

The first way we tried to set up, but all the same URLs are not displayed correctly.

In the second method - this option would come up for static pages, but the slave site will be updated continuously. what to do in this case?

Typically, the authors of some components still make an additional module for sef component to it was a normal component sef, but there is no such joomsef and how determined (by the rules) and the url so it appears to us

Rather than to create a hidden menu that point to a specific article, you can also do the slave with a category blog or similar.
This should improve a little the URL

You can modify Article Sharing component that normally handles the
URL, eg through Artio SEF?

There is no need to modify Joomla or create a specific stuff to modify the SEF.

Artio SEF is designed for that and inside Artio SEF, you can replace a URL by any other URL.
So do it with Artio SEF. This is its job to manage the SEF.