Department of Mathematics, Sokoto State University, Sokot, Nigeria. This paper presents the non-associative and non-commutative properties of the 123-avoiding patterns of Aunu permutation patterns.

Abstract: In constructing public-key cryptosystems, commutative property is an essential characteristic. Taking advantage of the commutative property of Chebyshev polynomials, a publickey cryptosystem ...

To include Non-commutative rings into the extended formula, it's essential to understand how they interact with tensor products and modules. Non-commutative rings are algebraic structures where ...

A line drawing of the Internet Archive headquarters building façade. An illustration of a magnifying glass. An illustration of a magnifying glass.