You have to have permission from the owner of the copyright to publish or re-publish their material. You can contact the magazine, try to work something out. Perhaps by structuring your page to point invitingly to their magazine they might welcome the traffic.
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Lots of people do this all the time. In some cases, it may be fair use. In others, it may not, but they just aren't getting caught. I'd be happy to discuss the situation with you further, if you're interested in retaining an attorney to review this sort of thing for your site -- my firm regularly handles copyright clearances similar to this.
The author is a Maryland attorney; however no answer given on Avvo is intended as legal advice or intended to create an attorney-client relationship. Dan's expertise lies in the electronic entertainment (video game) industry, as well as complex internet law issues, electronic free speech, entertainment law, copyright and trademark law, and computer fraud. He primarily represents game developers and founders of emergent internet technologies.
Giving credit to the magazine or the author--how do you know which owns the copyright--is generally not enough, in fact it does not help at all. Most likely you are at risk of suit since this will reduce the market for the magazine itself. I have an AVVO guide to fair use I will link to. Beyond that, I am available for consultation at 410-292-6989.
Licensed in Maryland with offices in Maryland and Oregon. Information here is general, does not create a lawyer-client relationship, and is not a substitute for consulting with an experienced attorney on the specifics of your situation.