The fundamental theorem of arithmetic says that any integer greater than 2 can be written uniquely as a product of primes. For the ring Z[√–5], although unique factorization holds for ideals, unique factorization fails for elements. We investigate both elements and ideals of Z[√–5]. For elements, we examine irreducibility (the analog of primality) in Z[√–5] and look at how often and how badly unique fac- torization fails. For ideals, we examine irreducibility again and a proof for unique factorization
Let A be a ring and a an ideal of A. In this paper we show how to construct factor rings A/ a and a ...
We establish necessary and sufficient conditions for a quadratic polynomial to be irreducible in the...
The main aim of this thesis is to produce and then study two generalizations of the unique factorisa...
The fundamental theorem of arithmetic says that any integer greater than 2 can be written uniquely a...
The fundamental theorem of arithmetic says that any integer greater than 2 can be written uniquely a...
The concept of unique factorization was first recognized in the 1840s, but even then, it was still f...
The ring of integers is a very interesting ring, it has the amazing property that each of its elemen...
Though it may seem non-intuitive, abstract algebra is often useful in the study of number theory. In...
In this paper, we give an elementary proof of the fact that the rings are unique factorization doma...
It is often taken it for granted that all positive whole numbers except 0 and 1 can be factored uniq...
AbstractThis paper gives an algorithm to factor a polynomialf(in one variable) over rings like Z/rZ ...
Let R be an infinite unique factorization domain with at most finitely many units. We discuss the in...
This informal document was motivated by a question here at my university by a bachelor student. I wi...
Includes abstract.Includes bibliographical references (leaves 92-95).This dissertation deals with al...
This thesis covers the factorization properties of number fields, and presents the structures necess...
Let A be a ring and a an ideal of A. In this paper we show how to construct factor rings A/ a and a ...
We establish necessary and sufficient conditions for a quadratic polynomial to be irreducible in the...
The main aim of this thesis is to produce and then study two generalizations of the unique factorisa...
The fundamental theorem of arithmetic says that any integer greater than 2 can be written uniquely a...
The fundamental theorem of arithmetic says that any integer greater than 2 can be written uniquely a...
The concept of unique factorization was first recognized in the 1840s, but even then, it was still f...
The ring of integers is a very interesting ring, it has the amazing property that each of its elemen...
Though it may seem non-intuitive, abstract algebra is often useful in the study of number theory. In...
In this paper, we give an elementary proof of the fact that the rings are unique factorization doma...
It is often taken it for granted that all positive whole numbers except 0 and 1 can be factored uniq...
AbstractThis paper gives an algorithm to factor a polynomialf(in one variable) over rings like Z/rZ ...
Let R be an infinite unique factorization domain with at most finitely many units. We discuss the in...
This informal document was motivated by a question here at my university by a bachelor student. I wi...
Includes abstract.Includes bibliographical references (leaves 92-95).This dissertation deals with al...
This thesis covers the factorization properties of number fields, and presents the structures necess...
Let A be a ring and a an ideal of A. In this paper we show how to construct factor rings A/ a and a ...
We establish necessary and sufficient conditions for a quadratic polynomial to be irreducible in the...
The main aim of this thesis is to produce and then study two generalizations of the unique factorisa...