This is the webpage for the manuscript that is currently entitled "Decompositions of Monomial Ideals" by W. Frank Moore, Mark Rogers and Sean Sather-Wagstaff. It is a draft of a mathematics textbook in abstract algebra for use at the advanced-undergraduate or graduate level. It is based on a course that Mark and Sean taught in the summer of 2006 as part of the IMMERSE program (Intensive Mathematics: a Mentoring, Education and Research Summer Experience) in the Department of Mathematics at the University of Nebraska-Lincoln.

Click here for the most current version of the text.

Revision history

Page numbers are of the form p(q) where p is the page number according to the header on the page and q is the page number according to the pdf-viewer (if your pdf-viewer does not recognize the difference).

• 14 Jan 2015: 204+xiii pp. Major reorganization and editing of entire text. New co-author.
• 22 Apr 11: 149+11 pp. Major reorganization and editing of entire text. New title. Computer exercises complete for Chapter 1. Main content is stable. Next revision will contain computer exercises for Chapters 2-7.
• 08 Apr 10: 149+10 pp. Minor editing of Chapters 1-2. Major reorganization and editing of remaining chapters.
• 05 Feb 10: 124+10 pp. Minor editing of Chapter 1. Major reorganization and editing of remaining chapters.
• 11 Jan 10: 112+10 pp. Minor editing of pages 1-3(11-13). Pages do not match with previous version on 1-10(11-20).
• 11 Jan 10: 112+10 pp. typos fixed on pages 1(11) and 2(12).
• 09 Jan 10: 112+10 pp. minor editing throughout; chapter enumeration changed from roman to arabic; split section on constructions with ideals in two; removed section on modular arithmetic; moved section on polynomial rings to earlier in Chapter 1, and redistributed some exercises to other sections; moved section on relations into Chapter 1; moved section on Noetherian rings to Chapter 2; moved section on corner elements to Chapter 3; moved section on irreducible ideals to Chapter 3.
• 23 Oct 08: 114+8 pp. Fixed minor typos throughout. Exercises added to Section III.2. Pages no longer match up with previous version starting on p. 86(94); pages re-synch on p. 95(103). New material begins with IV.1.8. Pages no longer match up with previous version starting on p. 98(106).
• 19 Oct 08: 108+8 pp. Fixed minor typos throughout. New material begins with IV.1.6. Pages no longer match up with previous version starting on p. 97(105).
• 14 Oct 08: 102+8 pp. Fixed minor typos throughout. New material begins with III.3.12. Pages no longer match up with previous version starting on p. 86(94).
• 12 Oct 08: 96+8 pp. Fixed minor typos throughout. Material in section III.2 has been augmented. Section III.3 is all new. Pages no longer match up with previous version starting on p. 85(93).
• 09 Oct 08: 92+8 pp. Fixed minor typos throughout. Proposition II.5.2 expanded. Pages no longer match up with previous version starting on p. 51(59); pages realign on p. 62(70). Items III.1.15-18 corrected. Material in section III.2 has been reorganized and augmented. Pages no longer match up with previous version starting on p. 72(80).
• 02 Oct 08: 92 pp. Fixed minor typos throughout. New material begins with III.1.16. Pages no longer match up with previous version starting on p. 71(79).
• 28 Sep 08: 86 pp. Fixed minor typos throughout. Chapter III reorganized and added to. Pages no longer match up with previous version starting on p. 67(75).
• 28 Sep 08: 82 pp. Fixed minor typos throughout. Added Exercises I.2.19, I.7.15-16, II.2.27, II.2.33, II.4.18, II.4.25-26. Edited Exercises II.2.29 and II.4.19. Added exercises in Section II.5. Material in Chapter III is all new. Pages no longer match up with previous version starting on p. 7(15); pages realign on p. 25(33). Pages no longer match up with previous version starting on p. 33(41).
• 25 Sep 08: 68 pp. Fixed minor typos throughout. Material in II.5.26-29 is new. Pages no longer match up with previous version starting on p. 60(68).
• 22 Sep 08: Fixed minor typos throughout. Material in II.5.22-25 is new. Pages no longer match up with previous version starting on p. 53(61).
• 18 Sep 08: Fixed minor typos throughout. Definition II.1.5 corrected. Removed Exercise from Section II.4. Section II.5 is all new. Pages no longer match up with previous version starting on p. 49(57).
• 14 Sep 08: 62 pp. Fixed minor typos throughout. Exercises are no longer in the TOC. (This causes the pages not to match up with the previous version starting on p. 5(13). Pages realign with previous version on p. 25(33).) Exercise I.5.12 edited. Exercises in Section II.2 edited. Remark II.3.11 added. Minor revisions in II.3.12, II.3.15, II.3.16, II.4.2. Added Exercise II.3.25. Major revisions after II.4.4. Pages no longer match up with previous version starting on p. 38(46).
• 11 Sep 08: 56 pp. Fixed minor typos throughout. New numbering protocol: all numbered items now of the form C.s.n where C is the chapter number, s is the section number and n is the item number. Added a part to I.3.13. Minor revisions in items II.2.11-II.2.26. Major revision in items after II.2.26. Pages no longer match up with previous version starting on p. 32(40).
• 08 Sep 08: 52 pp. Started tracking revisions.