Right Quotient Rings of a Right LCM Domain
1972 ◽
Vol 24
(5)
◽
pp. 983-988
◽
In this paper we continue our investigation of the class of right LCM domains which was introduced in [2]. A right LCM domain is an (not necessarily commutative) integral domain with unity in which the intersection of any two principal right ideals is again principal. In this note we study the right quotient rings of such a ring. In Section 1 we describe some of the characteristic properties of right quotient monoids with respect to which quotient rings are formed. Three particular types of quotient rings are described in Section 2. In Section 3 we relate the right ideals of a ring to those of its quotient ring.
2021 ◽
Vol 27
(1)
◽
pp. 75-89
2016 ◽
Vol 15
(08)
◽
pp. 1650149
◽
Keyword(s):
1971 ◽
Vol 14
(4)
◽
pp. 517-529
◽
Keyword(s):
1972 ◽
Vol 24
(4)
◽
pp. 703-712
◽
1977 ◽
Vol 24
(3)
◽
pp. 339-349
◽
Keyword(s):
1977 ◽
Vol 29
(5)
◽
pp. 914-927
◽
Keyword(s):
2016 ◽
Vol 95
(1)
◽
pp. 14-21
◽