It became more and more usual, from, say, the 1970s, for each book on Module Theory, to
point out and prove some (but in no more than 15 to 20 pages) generalizations to (mostly …

We give an elementary characterization of those (abelian) semigroups $ M $ that are direct
limits of countable sequences of finite direct products of monoids of the form $ C\cup\{0\} …

The present survey is devoted to results in the papers on lattice theory reviewed in
Referativnyi Zhurnal (Mat.) during 1965–1968, and is a natural continuation of Skornyakov's …

Let (T, , 1) be a monoid. A lattice L is called T-latice if it is provided with Page 1 MATHEMATICA,
Tome 40(63), N 2, 1998, pp. 155–158 PURITY IN T. LATTICES* GRIGORE CĂLUGĂREANU 1 …

Abstract In 1938 [6] Ore proved the following simple caracterization: the lattice of the
subgroups of a group is distributive iff every finite set of elements generates a cyclic group …

For a fully invariant subgroup A of an abelian group G= H⊕ K the equality A=(A∩ H)⊕(A∩
K) holds. This leads to a weaker definition of fully invariant elements in lattices. Among other …

Every commutative monoid M is endowed with its algebraic preordering, defined by x≤ y iff
there exists z∈ M such that x+ z= y, for all x, y∈ M. Then let x≡ y hold, if x≤ y≤ x. We …

In [4] T. HEAD gave a general definition of purity in complete lattices. In this note the pure
elements of the lattice of all the nonempty ideals of a lattice are investigated. 1. Introduction …

We give an elementary characterization of those abelian monoidsM that are direct limits of
countable sequences of finite direct sums of monoids of the form either (Z/nZ)⊔{0} or Z⊔{0} …

On characterizations of atomistic lattices Page 1 Algebra univers. 43 (2000) 031 – 039 0002–5240/00/010031
– 09 $ 1.50 + 0.20/0 © Birkhäuser Verlag, Basel, 2000 On characterizations of atomistic …