This book contains the definitions of several ring constructions used in various applications.
The concept of a groupoid-graded ring includes many of these constructions as special …

Publisher Summary This chapter highlights the radicals of graded rings. An important
problem in graded ring theory is to determine what information is of a graded nature. The …

The preservation of some ring properties by semilattice sums Page 1 COMMUNICATIONS
IN ALGEBRA, 15(5), 1017-1038 (1987) THE PRESERVATION OF SOME RING …

We show that if R is a, not necessarily unital, ring graded by a semigroup G equipped with
an idempotent e such that G is cancellative at e, the nonzero elements of eGe form a …

Bands of associative rings were introduced in 1973 by Weissglass. For the radicals playing
most essential roles in the structure theory (in particular, for those of Jacobson, Baer …

Let P be a semilattice. In (5), a ring T is called a supplementary semilattice sum of
subringsTα (α∈ P) if the following conditions hold: TαTβ⊆ Tαβ for all α, β∈ P, and for each …

When is the radical of a band sum of rings homogeneous? Page 1 COMMUNICATIONS IN
ALGEBRA, 18(2), 585-603 (1990) WHEN IS THE RADICAL OF A BAD SUM OF WGS …

Artinian band sums of rings Page 1 J. Austral. Math. Soc. (Series A) 58 (1995), 66-72
ARTINIAN BAND SUMS OF RINGS AV KELAREV (Received 18 June 1991; revised 29 April …

The concept of a semilattice sum of rings was introduced in [Q]. Let S be a semilattice, ie a
commutative semigroup consisting of idempotents. An associative ring R is called a …

Abstract\noindent We find the index of nilpotency of a strong supplementary semilattice sum
of rings, R=\tdsp ∑ α∈ YR α, where Y is a semilattice, when each R α has index of …