Abstract algebra | Ring theory
In abstract algebra, an element a of a ring R is called a left zero divisor if there exists a nonzero x in R such that ax = 0, or equivalently if the map from R to R that sends x to ax is not injective. Similarly, an element a of a ring is called a right zero divisor if there exists a nonzero y in R such that ya = 0. This is a partial case of divisibility in rings. An element that is a left or a right zero divisor is simply called a zero divisor. An element a that is both a left and a right zero divisor is called a two-sided zero divisor (the nonzero x such that ax = 0 may be different from the nonzero y such that ya = 0). If the ring is commutative, then the left and right zero divisors are the same. An element of a ring that is not a left zero divisor is called left regular or left cancellable. Similarly, an element of a ring that is not a right zero divisor is called right regular or right cancellable.An element of a ring that is left and right cancellable, and is hence not a zero divisor, is called regular or cancellable, or a non-zero-divisor. A zero divisor that is nonzero is called a nonzero zero divisor or a nontrivial zero divisor. A nonzero ring with no nontrivial zero divisors is called a domain. (Wikipedia).
Definition of a Zero Divisor with Examples of Zero Divisors
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Zero Divisor with Examples of Zero Divisors - Examples of zero divisors in Z_m the ring with addition modulo m and multiplication modulo m. Examples are done with Z_8 and Z_4. - Example of a zero divisor with the D
From playlist Abstract Algebra
Overview of Multiplicity of a zero - Online Tutor - Free Math Videos
👉 Learn about zeros and multiplicity. The zeroes of a polynomial expression are the values of x for which the graph of the function crosses the x-axis. They are the values of the variable for which the polynomial equals 0. The multiplicity of a zero of a polynomial expression is the number
From playlist Zeros and Multiplicity of Polynomials | Learn About
What are zeros of a polynomial
👉 Learn about zeros and multiplicity. The zeroes of a polynomial expression are the values of x for which the graph of the function crosses the x-axis. They are the values of the variable for which the polynomial equals 0. The multiplicity of a zero of a polynomial expression is the number
From playlist Zeros and Multiplicity of Polynomials | Learn About
What is the multiplicity of a zero?
👉 Learn about zeros and multiplicity. The zeroes of a polynomial expression are the values of x for which the graph of the function crosses the x-axis. They are the values of the variable for which the polynomial equals 0. The multiplicity of a zero of a polynomial expression is the number
From playlist Zeros and Multiplicity of Polynomials | Learn About
What is multiplicity and what does it mean for the zeros of a graph
👉 Learn about zeros and multiplicity. The zeroes of a polynomial expression are the values of x for which the graph of the function crosses the x-axis. They are the values of the variable for which the polynomial equals 0. The multiplicity of a zero of a polynomial expression is the number
From playlist Zeros and Multiplicity of Polynomials | Learn About
Overview of zeros of a polynomial - Online Tutor - Free Math Videos
👉 Learn about zeros and multiplicity. The zeroes of a polynomial expression are the values of x for which the graph of the function crosses the x-axis. They are the values of the variable for which the polynomial equals 0. The multiplicity of a zero of a polynomial expression is the number
From playlist Zeros and Multiplicity of Polynomials | Learn About
Learn how and why multiplicity of a zero make sense
👉 Learn about zeros and multiplicity. The zeroes of a polynomial expression are the values of x for which the graph of the function crosses the x-axis. They are the values of the variable for which the polynomial equals 0. The multiplicity of a zero of a polynomial expression is the number
From playlist Zeros and Multiplicity of Polynomials | Learn About
Abstract Algebra | Units and zero divisors of a ring.
We classify the units and zero divisors of Zn and the ring of 2x2 matrices with real entries. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
👉 Learn about zeros and multiplicity. The zeroes of a polynomial expression are the values of x for which the graph of the function crosses the x-axis. They are the values of the variable for which the polynomial equals 0. The multiplicity of a zero of a polynomial expression is the number
From playlist Zeros and Multiplicity of Polynomials | Learn About
Elliptic Curves - Lecture 6b - Divisors and differentials
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves
Schemes 35: Divisors on a Riemann surface
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we discuss the divisors on Riemann surfaces of genus 0 or 1, and show how the classical theory of elliptic functions determines the divisor cla
From playlist Algebraic geometry II: Schemes
Elliptic Curves - Lecture 9b - The (Picard) group law
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves
Schemes 37: Comparison of Weil and Cartier divisors
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we compare Cartier and Weil divisors, showing that for Noethernian integral schems the map from Cartier to Weil divisors is injective if the sc
From playlist Algebraic geometry II: Schemes
Schemes 36: Weil and Cartier divisors
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we define Weil and Cartier divisors and divisor classes, and give some simple examples of the groups of divisor classes.
From playlist Algebraic geometry II: Schemes
Elliptic Curves - Lecture 7 - Riemann-Roch, Hurwitz, and Weierstrass equations
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves
“Gauss sums and the Weil Conjectures,” by Bin Zhao (Part 6 of 8)
“Gauss sums and the Weil Conjectures,” by Bin Zhao. The topics include will Gauss sums, Jacobi sums, and Weil’s original argument for diagonal hypersurfaces when he raised his conjectures. Further developments towards the Langlands program and the modularity theorem will be mentioned at th
From playlist CTNT 2016 - ``Gauss sums and the Weil Conjectures" by Bin Zhao
Overview Zeros of a functions - Online Math Tutor - Free Math Videos
👉 Learn about zeros and multiplicity. The zeroes of a polynomial expression are the values of x for which the graph of the function crosses the x-axis. They are the values of the variable for which the polynomial equals 0. The multiplicity of a zero of a polynomial expression is the number
From playlist Zeros and Multiplicity of Polynomials | Learn About
Elliptic Curves - Lecture 12a - The Weil pairing (construction)
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves