http://starc.stthomas.ac.in:8080/xmlui/xmlui/handle/123456789/25 2026-04-20T13:50:51Z http://starc.stthomas.ac.in:8080/xmlui/xmlui/handle/123456789/421 CHARACTERISATION OF MODULES OVER PATH ALGEBRA Karthika, S; Viji, M Let K be a field, Q = (Q0, Q1) be a quiver and KQ be the generalised path algebra [10]. This paper gives a characterisation for the right and left modules over the path algebras of finite acyclic quiver. The study shows that the modules over such path algebras could be written as the decomposition of KQ-submodules. For KQ-modules over path algebras of quiver with countably many vertices, a sequence of KQ-submodules is identified which in finite case is a composition series. 2024-01-01T00:00:00Z http://starc.stthomas.ac.in:8080/xmlui/xmlui/handle/123456789/405 On quaternary resilient functions Parammel, Aboobacker; Viji, M. Functions on multiple valued logic are important tools for designing non-binary cryptographic algorithms. Cryptographic characteristics such as correlation immunity and resiliency of Boolean functions are well studied. This paper is on the resiliency of quaternary functions. We provide a method to extract a class quaternary 1-resilient functions in two variables using the group action of the permutation group S4. Using the resilient functions obtained, based on computational results using python programming language, we conjecture a technique to produce 1-resilient quaternary functions in three variables. We Also discuss orthogonal matrix characterizations of resilient functions on multiple valued logic. 2023-01-01T00:00:00Z http://starc.stthomas.ac.in:8080/xmlui/xmlui/handle/123456789/62 Unit elements in the path algebra of an acyclic quiver Karthika, S; Viji, M We investigate the algebraic properties of a particular non- commutative algebra, the path algebra, associated with a quiver. Quiver was initially introduced by Peter Gabriel. In this paper, we obtain a characterization for the invertibility of an element in the path algebra of an acyclic quiver. The study is an extension of the invertibility condition in a unique path quiver to acyclic quivers. 2021-06-10T00:00:00Z