2021
DOI: 10.3390/sym13112035
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A Note on the Connection between Ordered Semihyperrings

Abstract: The notion of ordered semihyperrings is a generalization of ordered semirings and a generalization of semihyperrings. In this paper, the Galois connection between ordered semihyperrings are studied in detail and various interesting results are obtained. A construction of an ordered semihyperring via a regular relation is given. Furthermore, we present the Galois connection between homomorphisms and derivations on an ordered semihyperring.

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Cited by 8 publications
(5 citation statements)
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“…For readers intrigued by the realm of hyperrings and desiring a deeper understanding, an extensive exploration can be found in the following scholarly sources: [9,15,16,18]. These references offer comprehensive insights into hyperrings, serving as valuable resources for those engaged in advanced studies or research endeavors within this domain.…”
Section: Applicationsmentioning
confidence: 99%
“…For readers intrigued by the realm of hyperrings and desiring a deeper understanding, an extensive exploration can be found in the following scholarly sources: [9,15,16,18]. These references offer comprehensive insights into hyperrings, serving as valuable resources for those engaged in advanced studies or research endeavors within this domain.…”
Section: Applicationsmentioning
confidence: 99%
“…In the ring Z 48 . Then U (Z 48 ) = {1, 5,7,11,13,17,19,23,25,29,31,35,37,41,43, 47}, N il(Z 48 ) = {0, 6, 12, 18, 24, 30, 36, 42}, Id(Z 48 ) = {0, 1, 16, 33}. By direct calculation, one easily check that Z 48 is a strongly 2-NC ring, with every unit is of order 4.…”
Section: Strongly 2-nc Rings With Units Of Order Twomentioning
confidence: 99%
“…In this paper, we define R as an associative ring containing an identity element. Finally, it is worth mentioning that ring theory has several applications in many field, see for example [11], [12] and [13]. To represent the set of units, idempotents and nilpotents in R, we will use the symbols U (R), Id(R) and N il(R), respectively.…”
Section: Introductionmentioning
confidence: 99%
“…Example 3. We consider the ordered semihyperring (R, +, •, ≤ R ) in Example 1 of [18] with two symmetrical hyperoperations + and •. Since x • y = {b, d} for all x, y ∈ R and ({b, d}] = R {b, d}, we observe that there do not exist proper 2-hyperideals in R.…”
Section: Construction Of Ordered (Semi)hyperrings Via W-pseudo-ordersmentioning
confidence: 99%