Special Topics in Algebra (MAE723)

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General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	MAE723
Semester	7
Course Title	Special Topics in Algebra
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 3, Credits: 6)
Course Type	Special Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes
Course Website (URL)	See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes	The principal aim of the course is to introduce the students to the main ideas and methods of Commutative Algebra.
General Competences	The course promotes inductive and creative thinking and aims to provide the student with the theoretical background and skills of commutative rings.

Syllabus

• Polynomial Rings
• Hilbert's Basis Theorem
• Localization
• Integral dependence
• Hilbert Series
• Dimension
• Groebner Bases
• Hilbert's Nullstellensatz Theorem

Teaching and Learning Methods - Evaluation

Delivery	Teaching on the blackboard by the teacher.
Use of Information and Communications Technology	Communication with the teacher by electronic means (i.e. e-mail).
Teaching Methods	Activity Semester Workload Lectures (13X3) 39 Personal study 78 Solving exercises 33 Course total 150
Student Performance Evaluation	Final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems.

Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

• J.Beachy, Introductory Lectures on Rings and Modules, LMS, Cambridge University Press, (1999).
• D.Dummit, R.M.Foote, Abstract Algebra, 3 edition, Prentice Hall, (2003).
• N.Jacobson, Basic Algebra I & II, W. H. Freeman and Company, (1985 & 1989).
• S.Lang, Algebra, Graduate Texts in Mathematics, Springer (2002).
• L.Rowen, Ring Theory, Academic Press, 2 edition (1991).
• Μαλιάκας. Ταλέλλη, Πρότυπα πάνω από Περιοχές Κυρίων Ιδεωδών και Εφαρμογές, Εκδ. Σοφία (2009).
• Α. Μπεληγιάννης, Μια Εισαγωγή στη Βασική Άλγεβρα, Εκδ. Κάλλιπος (2015).