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- Title
TWO SPACES OF MINIMAL PRIMES.
- Authors
BHATTACHARJEE, PAPIYA; Mundici, D.
- Abstract
This paper studies algebraic frames L and the set Min(L) of minimal prime elements of L. We will endow the set Min(L) with two well-known topologies, known as the Hull-kernel (or Zariski) topology and the inverse topology, and discuss several properties of these two spaces. It will be shown that Min(L) endowed with the Hull-kernel topology is a zero-dimensional, Hausdorff space; whereas, Min(L) endowed with the inverse topology is a T1, compact space. The main goal will be to find conditions on L for the spaces Min(L) and Min(L)-1 to have various topological properties; for example, compact, locally compact, Hausdorff, zero-dimensional, and extremally disconnected. We will also discuss when the two topological spaces are Boolean and Stone spaces.
- Subjects
PRIME numbers; TOPOLOGICAL spaces; ALGEBRAIC spaces; COMPACT spaces (Topology); MATHEMATICAL analysis; TOPOLOGY; SET theory
- Publication
Journal of Algebra & Its Applications, 2012, Vol 11, Issue 1, p1250014-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498811005373