New Structure of Skew Braces and Their Ideals
The primary motivation of this article is to introduce the definition of a strongly belonging element of a brace, presenting some results concerning the case where <i>I</i> acts as an ideal of a brace, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" di...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Computer Sciences & Mathematics Forum |
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| Online Access: | https://www.mdpi.com/2813-0324/7/1/54 |
| _version_ | 1827575159016390656 |
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| author | Mehsin Jabel Atteya |
| author_facet | Mehsin Jabel Atteya |
| author_sort | Mehsin Jabel Atteya |
| collection | DOAJ |
| description | The primary motivation of this article is to introduce the definition of a strongly belonging element of a brace, presenting some results concerning the case where <i>I</i> acts as an ideal of a brace, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>A</mi><mo>,</mo><mo>+</mo><mo>,</mo><mo>∘</mo><mo>)</mo></mrow></semantics></math></inline-formula>. We find that an element <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>∈</mo><mi>I</mi></mrow></semantics></math></inline-formula> acts as strongly belonging element of <i>I</i> when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>+</mo><mi>b</mi></mrow></semantics></math></inline-formula> yields <i>a</i> for all <i>b</i> in <i>I</i>. |
| first_indexed | 2024-03-08T20:52:14Z |
| format | Article |
| id | doaj.art-e3e2a768c0474a7780da988caaa934fd |
| institution | Directory Open Access Journal |
| issn | 2813-0324 |
| language | English |
| last_indexed | 2024-03-08T20:52:14Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computer Sciences & Mathematics Forum |
| spelling | doaj.art-e3e2a768c0474a7780da988caaa934fd2023-12-22T14:02:12ZengMDPI AGComputer Sciences & Mathematics Forum2813-03242023-05-01715410.3390/IOCMA2023-14601New Structure of Skew Braces and Their IdealsMehsin Jabel Atteya0Department of Mathematics, College of Education, Al-Mustansiriyah University, Baghdad P.O. Box 14022, IraqThe primary motivation of this article is to introduce the definition of a strongly belonging element of a brace, presenting some results concerning the case where <i>I</i> acts as an ideal of a brace, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>A</mi><mo>,</mo><mo>+</mo><mo>,</mo><mo>∘</mo><mo>)</mo></mrow></semantics></math></inline-formula>. We find that an element <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>∈</mo><mi>I</mi></mrow></semantics></math></inline-formula> acts as strongly belonging element of <i>I</i> when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>+</mo><mi>b</mi></mrow></semantics></math></inline-formula> yields <i>a</i> for all <i>b</i> in <i>I</i>.https://www.mdpi.com/2813-0324/7/1/54braceskew bracestrongly belonging elementleft brace |
| spellingShingle | Mehsin Jabel Atteya New Structure of Skew Braces and Their Ideals Computer Sciences & Mathematics Forum brace skew brace strongly belonging element left brace |
| title | New Structure of Skew Braces and Their Ideals |
| title_full | New Structure of Skew Braces and Their Ideals |
| title_fullStr | New Structure of Skew Braces and Their Ideals |
| title_full_unstemmed | New Structure of Skew Braces and Their Ideals |
| title_short | New Structure of Skew Braces and Their Ideals |
| title_sort | new structure of skew braces and their ideals |
| topic | brace skew brace strongly belonging element left brace |
| url | https://www.mdpi.com/2813-0324/7/1/54 |
| work_keys_str_mv | AT mehsinjabelatteya newstructureofskewbracesandtheirideals |