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Full-Text Articles in Mathematics
Upper Dimension And Bases Of Zero-Divisor Graphs Of Commutative Rings, S. Pirzada, M. Aijaza, Shane Redmond
Upper Dimension And Bases Of Zero-Divisor Graphs Of Commutative Rings, S. Pirzada, M. Aijaza, Shane Redmond
EKU Faculty and Staff Scholarship
For a commutative ring R with non-zero zero divisor set Z∗(R), the zero divisor graph of R is Γ(R) with vertex set Z∗(R), where two distinct vertices x and y are adjacent if and only if x y = 0. The upper dimension and the resolving number of a zero divisor graph Γ(R) of some rings are determined. We provide certain classes of rings which have the same upper dimension and metric dimension and give an example of a ring for which these values do not coincide. Further, we obtain some bounds for the upper dimension in zero divisor graphs …
Low-Dimensional Reality-Based Algebras, Rachel Victoria Barber
Low-Dimensional Reality-Based Algebras, Rachel Victoria Barber
Online Theses and Dissertations
In this paper we introduce the definition of a reality-based algebra (RBA) as well as a subclass of reality-based algebras, table algebras. Using sesquilinear forms, we prove that a reality-based algebra is semisimple. We look at a specific reality-based algebra of dimension 5 and provide formulas for the structure constants of this algebra. We determine by looking at these structure constants and setting conditions on specific structural components when this particular reality-based algebra is a table algebra. In fact, this will be a noncommutative table algebra of dimension 5.