Special multserial algebras are quotients of symmetric special multiserial algebras

TL;DR

This paper introduces a new definition for symmetric special multiserial algebras using defining cycles and proves that all special multiserial algebras are quotients of these symmetric algebras.

Contribution

It provides a novel characterization of symmetric special multiserial algebras and establishes a quotient relationship for all special multiserial algebras.

Findings

New definition of symmetric special multiserial algebras via defining cycles

Every special multiserial algebra is a quotient of a symmetric one

Abstract

In this paper we give a new definition of symmetric special multiserial algebras in terms of defining cycles. As a consequence, we show that every special multiserial algebra is a quotient of a symmetric special multiserial algebra.