Some Remarks on Rings

Lidia Obojska, and Paul O’Hara. "Some Remarks on Rings." Commentationes Mathematicae 50.1 (2010): null. <http://eudml.org/doc/292354>.

@article{LidiaObojska2010,
abstract = {Algebraic structures such as Rings, Fields, Boolean Algebras (Set Theory) and $\sigma $-Fields are well known and much has been written about them. In this paper we explore some properties of rings related to the distribution law. Specifically, we shall show that for rings there exists only one distribution law. Moreover, for the ring $(Z_\{p(p−1)n\} +, \cdot )$, where $(p, n) = 1$ there exist isomorphic groups $(G, +)$, $(H, \cdot )$, $G, H \subset Z_\{p(p−1)n\}$ of the order $(p − 1)$. Finally, we note that every ring $(Z_\{pn\}, +, \cdot )$ contains subfields $\text\{mod\}(pn)$.},
author = {Lidia Obojska, Paul O’Hara},
journal = {Commentationes Mathematicae},
keywords = {Distribution law; Rings; Isomorphism},
language = {eng},
number = {1},
pages = {null},
title = {Some Remarks on Rings},
url = {http://eudml.org/doc/292354},
volume = {50},
year = {2010},
}

TY - JOUR
AU - Lidia Obojska
AU - Paul O’Hara
TI - Some Remarks on Rings
JO - Commentationes Mathematicae
PY - 2010
VL - 50
IS - 1
SP - null
AB - Algebraic structures such as Rings, Fields, Boolean Algebras (Set Theory) and $\sigma $-Fields are well known and much has been written about them. In this paper we explore some properties of rings related to the distribution law. Specifically, we shall show that for rings there exists only one distribution law. Moreover, for the ring $(Z_{p(p−1)n} +, \cdot )$, where $(p, n) = 1$ there exist isomorphic groups $(G, +)$, $(H, \cdot )$, $G, H \subset Z_{p(p−1)n}$ of the order $(p − 1)$. Finally, we note that every ring $(Z_{pn}, +, \cdot )$ contains subfields $\text{mod}(pn)$.
LA - eng
KW - Distribution law; Rings; Isomorphism
UR - http://eudml.org/doc/292354
ER -