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I am a student studying Mathematics. I am looking for papers (in the field of abstract algebra) by a specific author. I wonder if there are standard ways, well-known strategies or methods you frequently use to find theses by a specific author. Any suggestions and recommendations will be helpful.

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What do you mean by "theses"? Two places for finding titles of Ph.D. theses (which you can then google the titles to find possible copies) is ProQuest and the Mathematics Genealogy Project. For papers and books, you can use MR Lookup for 1941-present (if you actually have access to Mathematical Reviews, then you can pretty much find anything), and zbMath for 1931-present, and Jahrbuch Database for 1868-1942, and EuDML, and google scholar, and WorldCat, and arXiv.org for math. Also, there are quite a few more limited resources for information about mathematicians and papers, such as the All-Russian Mathematical Portal, and the MacTutor History of Mathematics archive, and the Czech Digital Mathematics Library, and the French digital mathematics library, and French Ph.D. theses from 1910 to 1949, to give just a few of the very many such sites.