The First Isomorphism Theorem and Other Properties of Rings
Keyword(s):
Summary Different properties of rings and fields are discussed [12], [41] and [17]. We introduce ring homomorphisms, their kernels and images, and prove the First Isomorphism Theorem, namely that for a homomorphism f : R → S we have R/ker(f) ≅ Im(f). Then we define prime and irreducible elements and show that every principal ideal domain is factorial. Finally we show that polynomial rings over fields are Euclidean and hence also factorial
2004 ◽
Vol 111
(2)
◽
pp. 150-152
◽
Keyword(s):
Keyword(s):
1971 ◽
Vol 5
(1)
◽
pp. 87-94
◽
Keyword(s):
1991 ◽
Vol 157
◽
pp. 141-145
◽
1969 ◽
Vol 10
(3-4)
◽
pp. 395-402
◽
Keyword(s):
1991 ◽
Vol 12
(3)
◽
pp. 581-591
◽