交换幺半群同余与二项式理想的分解
交换代数
2015-09-11 v5 组合数学
摘要
交换幺半群同余的准素分解对交换环中准素分解的某些特征不敏感。这些特征被本文引入的更精细的 mesoprimary 同余分解理论所捕捉，该理论配有见证元与关联素对象。mesoprimary 分解的组合理论可提升至幺半群代数中的任意二项式理想。由此得到的二项式 mesoprimary 分解是二项式理想的一种新型交分解，具有计算效率高且独立于基域假设的优点。二项式准素分解可容易地从 mesoprimary 分解中恢复。
引用
@article{arxiv.1107.4699,
title = {Decompositions of commutative monoid congruences and binomial ideals},
author = {Thomas Kahle and Ezra Miller},
journal= {arXiv preprint arXiv:1107.4699},
year = {2015}
}
备注
62 pages, 7 figures, v2: small improvements over v1, v3: added Problem 17.7, Corollary 4.15 and other small refinements, v4: major revision: definition of witness adjusted (Section 4), and incorrect claims concerning binomial irreducible decomposition excised (Section 15), v5: various corrections and improvements. Final version, accepted by Algebra and Number Theory