Universal Algebra

To join this course, write to the course instructor, Dr. Purbita Jana

Welcome to the Universal Algebra Course. In this course I would like to focus on order algebraic structures and then fundamental notions of Universal Algebra. Also I would like to talk about Stone Duality and other important dualities. Depending on the interest I'll focus on MV-Algebra and its connections with other mathematical structures in more details.

I'll appreciate highly interactive and jovial sessions so that we will enrich our knowledge from both sides.

References:

1. Lattice Theory by G. Birkhoff

2. A Course in Universal Algebra by Stanley Burris and H.P.Sankappanavar (https://www.math.uwaterloo.ca/~snburris/htdocs/UALG/univ-algebra.pdf)

3. Algebraic Foundations of Many-Valued Reasoning by R.L.Cignoli, Itala M. d'Ottaviano, Daniel Mundici.

Universal algebra regular participants

Lecture 1: Sunday, 2 August 2020, at 4:00pm IST

Introduction to Lattice and other Ordered Algebraic Structures.

Slide

Lecture 2: Sunday, 9 August 2020, at 4:00pm IST

Some Basic ideas on Lattice Theory

Slide

Lecture 3: Sunday, 16 August 2020, at 4:00pm IST

Boolean Algebra, Heyting Algebra

Slide

Lecture 4: Sunday, 23 August 2020, at 4:00pm IST

Notion of algebras, homomorphisms and subalgebras

Slide

Lecture 5: Sunday, 30 August 2020, at 4:00pm IST

Subalgebras, direct products, congruence relations

Slide

Lecture 6: Sunday, 6 September 2020, at 4:00pm IST

Congruence relations, homomorphism theorem

Slide

Lecture 7: Sunday, 13 September 2020, at 4:00pm IST

Subdirect products

Slide

Lecture 8: Sunday, 20 September 2020, at 4:00pm IST

Free algebras, Class of algebras

Slide

Lecture 9: Sunday, 27 September 2020, at 4:00pm IST

Subdirect product theorem, Free algebras

Slide

Lecture 10: Sunday, 11 October 2020, at 4:00pm IST

Proof of subdirect product theorem

Slide

Lecture 11: Sunday, 18 October 2020, at 4:00pm IST

Birkhoff's characterisation theorem of variety

Slide

Lecture 12: Saturday, 24 October 2020, at 4:00pm IST

Basics of category theory and categorical view of algebraic structures

Lecture 13: Sunday, 1 November 2020, at 4:00pm IST

Many valued algebra and Stone duality