2011/01/12 by Jesse Elliott, Elliott, Jesse · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.AC #math.RA
paper · pdf · doi:10.48550/arxiv.1101.2462
37 pages; replaces an earlier paper that was withdrawn (arXiv:1002.3451)
arxiv created 2011/01/12 · openalex publication_date 2011/01/12 · arxiv updated 2011/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that a generalization of quantales and prequantales provides a noncommutative and nonassociative abstract ideal theoretic setting for the theories of star operations, semistar operations, semiprime operations, ideal systems, and module systems, and conversely the latter theories motivate new results on quantales and prequantales. Results include representation theorems for precoherent prequantales and multiplicative semilattices; a characterization of the simple prequantales; and a generalization to the setting of precoherent prequantales of the construction of the largest finite type semistar operation and the largest stable semistar operation smaller than a given semistar operation.