## Description

A frame is a complete lattice that satisfies a strong distributive law, known as the frame law. Frames are also known as Pointfree Topology, as every topology is a frame. Even though the concept of frames originated from topology, the idea has expanded to many other areas of mathematics and frames are now studied in their own merit. Given two frame L and M, we say M is an extension of L if L is a subframe of M. In this talk we will discuss different types of frames extensions, such as Rigid extension, r-extension, and r*-extension between two frames. We will show the relation between these extensions and how they are related to the prime elements of the frames.

## Date of Event

Tuesday, April 16, 2024

## Location

Parker Building Room 338

#### Included in

Extensions of Algebraic Frames

Parker Building Room 338

A frame is a complete lattice that satisfies a strong distributive law, known as the frame law. Frames are also known as Pointfree Topology, as every topology is a frame. Even though the concept of frames originated from topology, the idea has expanded to many other areas of mathematics and frames are now studied in their own merit. Given two frame L and M, we say M is an extension of L if L is a subframe of M. In this talk we will discuss different types of frames extensions, such as Rigid extension, r-extension, and r*-extension between two frames. We will show the relation between these extensions and how they are related to the prime elements of the frames.

## Presenter Bio

Dr. Bhattacharjee is a Senior Instructor in the Mathematics department at FAU. She received her Ph.D. in Mathematics from Bowling Green State University and is a former tenured professor from Penn State Behrend. Dr. Bhattacharjee is active in mathematical research and is the Ph.D. advisor of two FAU graduate students; her research interest includes Ordered Algebraic Structures, theories of Frames, L-Groups, and Rings of Continuous Functions. She is also the first faculty at FAU to receive the United State Distance Learning Association's (USDLA) Innovation Award.