In:
Discrete Mathematics, Algorithms and Applications, World Scientific Pub Co Pte Ltd, Vol. 11, No. 01 ( 2019-02), p. 1950010-
Abstract:
Let [Formula: see text] be a commutative ring with identity and [Formula: see text] , a fixed integer. Let [Formula: see text] be the set of all [Formula: see text] -maximal elements in [Formula: see text] Associate a [Formula: see text] -maximal hypergraph [Formula: see text] to [Formula: see text] with vertex set [Formula: see text] and for distinct elements [Formula: see text] in [Formula: see text], the set [Formula: see text] is an edge of [Formula: see text] if and only if [Formula: see text] and [Formula: see text] for all [Formula: see text] . In this paper, we determine all isomorphism classes of finite commutative non-local rings with identity whose [Formula: see text]-maximal hypergraph has genus one. Finally, we classify all finite commutative non-local rings [Formula: see text] for which [Formula: see text] is projective.
Type of Medium:
Online Resource
ISSN:
1793-8309
,
1793-8317
DOI:
10.1142/S1793830919500101
Language:
English
Publisher:
World Scientific Pub Co Pte Ltd
Publication Date:
2019