If you want to know whether your Rich Snippets have errors you can use Google's testing tools: [search.google.com...]

You may find helpful information in this similar discussion: [webmasterworld.com...]

Note that Google has moved from the old Schema structured data formats to the use of "Rich Snippets". They announced the move last July: [webmasters.googleblog.com...]

...but on the SERP page is appearing without rich snippet.

Serious_Joker, welcome to WebmasterWorld. From your initial posts here, I'm guessing that you might think that search is more mechanical than it is... ie, if you fulfill certain mechanical requirements, you will rank... or that a certain Google feature will display. It's not so precise as that, and I think that Google takes pains to make that clear, but I'm seeing that there are many pages of documentation, and it's possible to have read some of it without seeing all of it...

Here's a Google Developers guide that should give you a good introduction to what you can expect from structured data in general, not just in Rich Snippets. I'm going to quote and highlight several points on the page that I feel probably apply to your situation...

General structured data guidelines
[developers.google.com...]

These guidelines must be followed to enable structured data to be eligible for inclusion in Google Search results.

In other words, if you've followed the guidelines and implemented the suggestions correctly, you become eligible to be considered for rich results. Google makes it clear that this doesn't automatically mean that such results will be displayed...

Important: Google does not guarantee that your structured data will show up in search results, even if your page is marked up correctly according to the Rich Results Test. Here are some common reasons why:
- Using structured data enables a feature to be present, it does not guarantee that it will be present. The Google algorithm tailors search results to create what it thinks is the best search experience for a user, depending on many variables, including search history, location, and device type. In some cases it may determine that one feature is more appropriate than another, or even that a plain blue link is best..... (etc)

These are the main points in the first paragraph of many points on a long page. I suggest you read the whole Google article carefully.

You say in your post: "it's been more than a month", but you don't say what 'it" is. Is this month the length of time that the domain and page have been online? ...that the page has been in Google's index? ...or simply the time since you have added the rich snippet markup?

Where is your page currently ranking for your target query in the serp?

Roughly, without getting into specifics, what kind of page is it? How competitive is it? How has the site been promoted? Etc etc.

Have you looked at the quality of the pages that are above you, and tried to figure out why Google is ranking them before you?

Rich snippets questions have been asked for years, and I'm assuming that Google to award them only to the best of the best, but I haven't recently assessed that. Generally, for a page to have rich snippets or be featured up top, it would need to be ranking in the top 10 for your query... and then one looks at other aspects of why it's in a rich snippet or featured result.

If the site has been online for only a month, that is not nearly enough time. I'll leave that for others to discuss with you.

This part of what Robert said is all you have to know:

"...if you've followed the guidelines and implemented the suggestions correctly, you become eligible to be considered for rich results. Google makes it clear that this doesn't automatically mean that such results will be displayed..."

Adding structured data that validates does not guarantee a rich results. It only makes you eligible for rich results if Google chooses to show them from your site.

There are other factors that can cause a site to be ineligible, despite implementing validated structured data.