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Full-Text Articles in Algebra
Permutation Groups And Puzzle Tile Configurations Of Instant Insanity Ii, Amanda N. Justus
Permutation Groups And Puzzle Tile Configurations Of Instant Insanity Ii, Amanda N. Justus
Electronic Theses and Dissertations
The manufacturer claims that there is only one solution to the puzzle Instant Insanity II. However, a recent paper shows that there are two solutions. Our goal is to find ways in which we only have one solution. We examine the permutation groups of the puzzle and use modern algebra to attempt to fix the puzzle. First, we find the permutation group for the case when there is only one empty slot at the top. We then examine the scenario when we add an extra column or an extra row to make the game a 4 × 5 puzzle or …
Polynomial Factoring Algorithms And Their Computational Complexity, Nicholas Cavanna
Polynomial Factoring Algorithms And Their Computational Complexity, Nicholas Cavanna
Honors Scholar Theses
Finite fields, and the polynomial rings over them, have many neat algebraic properties and identities that are very convenient to work with. In this paper we will start by exploring said properties with the goal in mind of being able to use said properties to efficiently irreducibly factorize polynomials over these fields, an important action in the fields of discrete mathematics and computer science. Necessarily, we must also introduce the concept of an algorithm’s speed as well as particularly speeds of basic modular and integral arithmetic opera- tions. Outlining these concepts will have laid the groundwork for us to introduce …
Algebraic Structures On Fuzzy Unit Square And Neutrosophic Unit Square, Florentin Smarandache, W.B. Vasantha Kandasamy
Algebraic Structures On Fuzzy Unit Square And Neutrosophic Unit Square, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors build algebraic structures on fuzzy unit semi open square UF = {(a, b) | a, b [0, 1)} and on the fuzzy neutrosophic unit semi open square UN = {a + bI | a, b [0, 1)}. This study is new and we define, develop and describe several interesting and innovative theories about them. We cannot build ring on UN or UF. We have only pseudo rings of infinite order. We also build pseudo semirings using these semi open unit squares. We construct vector spaces, S-vector spaces and strong pseudo special vector space using …
Algebraic Structures On Real And Neutrosophic Semi Open Squares, Florentin Smarandache, W.B. Vasantha Kandasamy
Algebraic Structures On Real And Neutrosophic Semi Open Squares, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
Here for the first time we introduce the semi open square using modulo integers. Authors introduce several algebraic structures on them. These squares under addition modulo ‘n’ is a group and however under product this semi open square is only a semigroup as under the square has infinite number of zero divisors. Apart from + and we define min and max operation on this square. Under min and max operation this semi real open square is a semiring. It is interesting to note that this semi open square is not a ring under + and since …