MathSciNet is another good way to look for published articles about Algebra by faculty and students from the University of Illinois at Urbana-Champaign. The links below search MathSciNet using Institution Code, 1-IL (Department of Mathematics, University of Illinois at Urbana-Champaign), and  Mathematics Subject Classification (MSC) Primary classifications related to Algebra:

• 06 (Order, lattices, ordered algebraic structures)
• 12 (Field theory and polynomials)
• 13 (Commutative algebra)
• 15 (Linear and multilinear algebra; matrix theory)
• 16 (Associative rings and algebras)
• 17 (Nonassociative rings and algebras)
• 18 (Category theory; homological algebra)
• 19 (K-theory)
• 20 (Group theory and generalizations)
• 55 (Algebraic topology)