| Articolul precedent |
| Articolul urmator |
 |
 256 6 |
| Ultima descărcare din IBN: 2023-11-15 14:18 |
 SM ISO690:2012CHIRIAC, Liubomir, BOBEICĂ, Natalia. On some non-isomorphic quasigroups of small order. In: Conference on Applied and Industrial Mathematics: CAIM 2022, Ed. 29, 25-27 august 2022, Chişinău. Chișinău, Republica Moldova: Casa Editorial-Poligrafică „Bons Offices”, 2022, Ediţia a 29, pp. 144-147. ISBN 978-9975-81-074-6. |
| EXPORT metadate: Google Scholar Crossref CERIF DataCite Dublin Core |
| Conference on Applied and Industrial Mathematics Ediţia a 29, 2022 |
||||||
|
Conferința "Conference on Applied and Industrial Mathematics" 29, Chişinău, Moldova, 25-27 august 2022 | ||||||
|
||||||
| Pag. 144-147 | ||||||
|
||||||
 Descarcă PDF |
||||||
| Rezumat | ||||||
A non-empty set G is said to be a groupoid relatively to a binary operation denoted by {·}, if for every ordered pair (a, b) of elements of G there is a unique element ab ∈ G. A groupoid (G, ·) is called a quasigroup if for every a, b ∈ G the equations a · x = b and y · a = b have unique solutions. We consider the quasigroups of properties (∗): left distributive, right distributive, left Bol, right Bol, left involutary, right involutary, left semimedial, right semimedial, left cancellative, right cancellative, non-associative loops, medial, paramedial, Ward, Cote and Manin quasigroups. We examine the following problem: Problem 1. How many non-isomorphic quasigroups of properties (∗) of order 3, 4, 5, 6, 7 do there exist? We have elaborated algorithms for generating and enumerating non-isomorphic quasigroups of small order of properties (∗). The results established here are related to the work in ([1,2,3,4,5]). Applying the algorithms elaborated, we prove the following results: |
||||||
|
Cerif XML Export
<?xml version='1.0' encoding='utf-8'?>
<CERIF xmlns='urn:xmlns:org:eurocris:cerif-1.5-1' xsi:schemaLocation='urn:xmlns:org:eurocris:cerif-1.5-1 http://www.eurocris.org/Uploads/Web%20pages/CERIF-1.5/CERIF_1.5_1.xsd' xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' release='1.5' date='2012-10-07' sourceDatabase='Output Profile'>
<cfResPubl>
<cfResPublId>ibn-ResPubl-170289</cfResPublId>
<cfResPublDate>2022</cfResPublDate>
<cfVol>Ediţia a 29</cfVol>
<cfStartPage>144</cfStartPage>
<cfISBN>978-9975-81-074-6</cfISBN>
<cfURI>https://ibn.idsi.md/ro/vizualizare_articol/170289</cfURI>
<cfTitle cfLangCode='EN' cfTrans='o'>On some non-isomorphic quasigroups of small order</cfTitle>
<cfAbstr cfLangCode='EN' cfTrans='o'><p>A non-empty set G is said to be a groupoid relatively to a binary operation denoted by {·}, if for every ordered pair (a, b) of elements of G there is a unique element ab ∈ G. A groupoid (G, ·) is called a quasigroup if for every a, b ∈ G the equations a · x = b and y · a = b have unique solutions. We consider the quasigroups of properties (∗): left distributive, right distributive, left Bol, right Bol, left involutary, right involutary, left semimedial, right semimedial, left cancellative, right cancellative, non-associative loops, medial, paramedial, Ward, Cote and Manin quasigroups. We examine the following problem: Problem 1. How many non-isomorphic quasigroups of properties (∗) of order 3, 4, 5, 6, 7 do there exist? We have elaborated algorithms for generating and enumerating non-isomorphic quasigroups of small order of properties (∗). The results established here are related to the work in ([1,2,3,4,5]). Applying the algorithms elaborated, we prove the following results:</p></cfAbstr>
<cfResPubl_Class>
<cfClassId>eda2d9e9-34c5-11e1-b86c-0800200c9a66</cfClassId>
<cfClassSchemeId>759af938-34ae-11e1-b86c-0800200c9a66</cfClassSchemeId>
<cfStartDate>2022T24:00:00</cfStartDate>
</cfResPubl_Class>
<cfResPubl_Class>
<cfClassId>e601872f-4b7e-4d88-929f-7df027b226c9</cfClassId>
<cfClassSchemeId>40e90e2f-446d-460a-98e5-5dce57550c48</cfClassSchemeId>
<cfStartDate>2022T24:00:00</cfStartDate>
</cfResPubl_Class>
<cfPers_ResPubl>
<cfPersId>ibn-person-715</cfPersId>
<cfClassId>49815870-1cfe-11e1-8bc2-0800200c9a66</cfClassId>
<cfClassSchemeId>b7135ad0-1d00-11e1-8bc2-0800200c9a66</cfClassSchemeId>
<cfStartDate>2022T24:00:00</cfStartDate>
</cfPers_ResPubl>
<cfPers_ResPubl>
<cfPersId>ibn-person-18407</cfPersId>
<cfClassId>49815870-1cfe-11e1-8bc2-0800200c9a66</cfClassId>
<cfClassSchemeId>b7135ad0-1d00-11e1-8bc2-0800200c9a66</cfClassSchemeId>
<cfStartDate>2022T24:00:00</cfStartDate>
</cfPers_ResPubl>
</cfResPubl>
<cfPers>
<cfPersId>ibn-Pers-715</cfPersId>
<cfPersName_Pers>
<cfPersNameId>ibn-PersName-715-3</cfPersNameId>
<cfClassId>55f90543-d631-42eb-8d47-d8d9266cbb26</cfClassId>
<cfClassSchemeId>7375609d-cfa6-45ce-a803-75de69abe21f</cfClassSchemeId>
<cfStartDate>2022T24:00:00</cfStartDate>
<cfFamilyNames>Chiriac</cfFamilyNames>
<cfFirstNames>Liubomir</cfFirstNames>
</cfPersName_Pers>
</cfPers>
<cfPers>
<cfPersId>ibn-Pers-18407</cfPersId>
<cfPersName_Pers>
<cfPersNameId>ibn-PersName-18407-3</cfPersNameId>
<cfClassId>55f90543-d631-42eb-8d47-d8d9266cbb26</cfClassId>
<cfClassSchemeId>7375609d-cfa6-45ce-a803-75de69abe21f</cfClassSchemeId>
<cfStartDate>2022T24:00:00</cfStartDate>
<cfFamilyNames>Bobeică</cfFamilyNames>
<cfFirstNames>Natalia</cfFirstNames>
</cfPersName_Pers>
</cfPers>
</CERIF>|
|
|
