Set relations and set systems induced by some families of integral domains

Chiaselotti, Giampiero; Infusino, Federico; Oliverio, Paolo Antonio

doi:10.1016/j.aim.2020.106999

Cited by 13 publications

(2 citation statements)

References 55 publications

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“…These posets generalize the classical Boolean algebras [23,38], and in literature they are studied in several different mathematical contexts (see for example [1,11,16,19,25,26,30,31,36,37]). In this paper we use involution posets in a set operatorial perspective, in analogy with what has been recently done for integral domains [14] and monoid actions [15]. Our basic motivation arises from an extremal combinatorial sum problem studied in [12] and in [13].…”

Section: Introductionmentioning

confidence: 99%

Real subset sums and posets with an involution

Bisi

Chiaselotti

Gentile

2021

Int. J. Algebra Comput.

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In this paper, we carry out in an abstract order context some real subset combinatorial problems. Specifically, let [Formula: see text] be a finite poset, where [Formula: see text] is an order-reversing and involutive map such that [Formula: see text] for each [Formula: see text]. Let [Formula: see text] be the Boolean lattice with two elements and [Formula: see text] the family of all the order-preserving 2-valued maps [Formula: see text] such that [Formula: see text] if [Formula: see text] for all [Formula: see text]. In this paper, we build a family [Formula: see text] of particular subsets of [Formula: see text], that we call [Formula: see text]-bases on [Formula: see text], and we determine a bijection between the family [Formula: see text] and the family [Formula: see text]. In such a bijection, a [Formula: see text]-basis [Formula: see text] on [Formula: see text] corresponds to a map [Formula: see text] whose restriction of [Formula: see text] to [Formula: see text] is the smallest 2-valued partial map on [Formula: see text] which has [Formula: see text] as its unique extension in [Formula: see text]. Next we show how each [Formula: see text]-basis on [Formula: see text] becomes, in a particular context, a sub-system of a larger system of linear inequalities, whose compatibility implies the compatibility of the whole system.

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Section: Introductionmentioning

confidence: 99%

Real subset sums and posets with an involution

Bisi

Chiaselotti

Gentile

2021

Int. J. Algebra Comput.

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“…Recently, the interrelations between rough set theory and various branches of mathematics, such as combinatorics [12], monoids [10], matroids [15,23,24,25], groups [7,18], integral domains [11] and modules [9] has been deeply studied and constitute a research field which is developing rapidly. In our perspective, we are interested in the interrelations between rough set theory and groups.…”

Section: Introductionmentioning

confidence: 99%

Rough action on topological rough groups

et al. 2020

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<p>In this paper we explore the interrelations between rough set theory and group theory. To this end, we first define a topological rough group homomorphism and its kernel. Moreover, we introduce rough action and topological rough group homeomorphisms, providing several examples. Next, we combine these two notions in order to define topological rough homogeneous spaces, discussing results concerning open subsets in topological rough groups.</p>

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On a quotient S-set induced by countably infinite decreasing chains

Infusino

2022

Ann Univ Ferrara

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Set relations and set systems induced by some families of integral domains

Cited by 13 publications

References 55 publications

Real subset sums and posets with an involution

Real subset sums and posets with an involution

Rough action on topological rough groups

On a quotient S-set induced by countably infinite decreasing chains

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