… regular or self-injective regular rings with non-zero socle are characterised in terms of a
special maximal ideal which acts as a “test module” Rings … or flatand biregular rings are also …

… maximal ideal m and fraction field then a prime divisor of Ä is a valuation of whose valuation
ring dommates R (ie Rc Rv and mcm^, the maximal ideal … Thus is a maximal ideal in S, and …

… regular in the ring A. We shall show that the join of all regular ideals in an arbitrary ring R
is a regular ideal, and hence that there exists a unique maximal regular ideal M= M(R) in R. …

… Corollary to (1) and (2) is the confirmation, for the case of maximal ideals, of one of the …
Corollary to (3) is that for R regular and n > 1, every maximal ideal of A is generated by a regular …

… ideal is a maximal ideal in a commutative ring Ρ with identity, then we say that I? is a P-ring. …
of all maximal ideals does all that an ascending chain condition can, and thus make the …

… ring 9D in which every ideal has a finite basis and in which the set m of all non-units is an
ideal, necessarily maximal. … local ring is a homomorphic image of a complete regular local ring. …

… rings are semiregular and π-regular rings, and the endomorphism … regular ring without
minimal nonzero ideals. Let M be a maximal ideal of R, k be the field R/M, and let A be the ring ( …

… we discuss the maximal ideals and some structure spaces of an ideal of C… ideal 7 of C(X),
the maximal ideals of 7 are precisely those ideals of the form 7 n M where M is a maximal ideal …

… McCoy showed that every (not necessarily commutative) ring $R$ has an ideal $\frak M (R)$
consisting of elements $a$ for which there is an $x$ such that $axa=a$, and maximal with …

… f-rings with identity element, of a maximal !-ideal having finite … f-rings with identity element in
which every maximal !-ideal has … it is possible for commutative semiprime f-rings with identity …