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Many associated primes of powers of primes
Institution:1. Department of Mathematics, UCSD, La Jolla, CA 92093-0112, United States of America;2. Reed College, 3203 SE Woodstock Boulevard, Portland, OR 97202, United States of America;1. Matematika Saila, Euskal Herriko Unibertsitatearen Zientzia eta Teknologia Fakultatea, posta-kutxa 644, 48080 Bilbo, Spain;2. Departamento de Matemáticas, Facultad de Ciencia y Tecnología de la Universidad del País Vasco, Apdo correos 644, 48080 Bilbao, Spain;1. Department of Mathematics, Wellesley College, Wellesley, MA 02481, United States of America;2. Department of Mathematics, Brandeis University, Waltham, MA 02454, United States of America;1. Institute of Mathematics, VAST, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam;2. Department of Mathematics, FPT University, Hanoi, Vietnam;3. Department of Mathematics Teacher Education, Dong Thap University, Vietnam;1. Charles University Prague, Czechia;2. Loyola Marymount University, United States of America;3. Harvard University, United States of America
Abstract:We construct families of prime ideals in polynomial rings for which the number of associated primes of the second power (or higher powers) is exponential in the number of variables in the ring.
Keywords:Primary decomposition  Powers of ideals  Rees algebra  Extended Rees algebra  Rees-like algebra  Polynomial rings
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