… This theory, which may be described in many equivalent ways ([6], [9]) is for our present
purposes best considered as the homology of a certain normalized "cubical" complex Q(G), …

… an R-module satisfies certain conditions, then it is in fact acommutative ring extension of R.
We … Using the results of 1 we show that U is a commutative ring extension of R contained in E; …

… paper rings will be all commutative rings with units and morphisms will mean unitary ring-…
In §3, we shall discuss incomparability for some special ring extensions. In Corollary 3.2, we …

… The next two results consider the possible validity of the analogue of Theorem 2.1 for certain
kinds of ring extensions R ⊂ S where the base ring R may be infinite and S is still assumed …

… Integral minimal ring extensions are thereby classified in three types, which are called inert,
decomposed, and ramified, respectively. All the minimal ring extensions discussed in this …

… We discuss and show when certain rings are (or are not) right Osofsky compatible. … describe
ring hulls of monoid and matrix ring extensions belonging to the various classes of rings we …

… In most of this paper we assume that r2 = 0 and that A is a trivial extension A/r K r (see …
a new artin ring F, which under certain conditions will have A as a factor ring in a natural way…

… If the three functions satisfy certain conditions, R is an extension of … ring extensions, we must
consider an extension of a ring A by a ring B as a triple (q~, R, ~) rather than as a single.ring. …

… This formula is illustrated in Example 3.8, while Example 3.9 illustrates how our methods
apply to calculate the lower bound in question for certain finite SPIRs which are not prime rings. …

… By a minimal overring of R, we mean any overring of R which is a minimal ring extension
of … the study of minimal ring extensions reduces to considering extensions of reduced rings. …