A class of hyperrings and hyperfields
Hyperring is a structure generalizing that of a ring, but where the addition is not a composition, but a hypercomposition, i.e., the sum x+y of two elements, x,y, of a hyperring H is, in general, not an element but a subset of H. When the non-zero elements of a hyperring form a multiplicative group,...
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| Format: | Article |
| Language: | English |
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Wiley
1983-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171283000265 |
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| _version_ | 1832551551458082816 |
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| author | Marc Krasner |
| author_facet | Marc Krasner |
| author_sort | Marc Krasner |
| collection | DOAJ |
| description | Hyperring is a structure generalizing that of a ring, but where the addition is not a composition, but a hypercomposition, i.e., the sum x+y of two elements, x,y, of a hyperring H is, in general, not an element but a subset of H. When the non-zero elements of a hyperring form a multiplicative group, the hyperring is
called a hyperfield, and this structure generalizes that of a field. A certain class of hyperfields (residual hyperfields of valued fields) has been used by the author [1] as an important technical tool in his theory of approximation of complete valued fields by sequences of such fields. Tne non-commutative theory of hyperrings (particularly Artinian) has been studied in depth by Stratigopoulos [2]. |
| format | Article |
| id | doaj-art-86895088f2ef42b79276805ba9912f60 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1983-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-86895088f2ef42b79276805ba9912f602025-02-03T06:01:16ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251983-01-016230731110.1155/S0161171283000265A class of hyperrings and hyperfieldsMarc Krasner0Université de Paris VI, Paris 75006, FranceHyperring is a structure generalizing that of a ring, but where the addition is not a composition, but a hypercomposition, i.e., the sum x+y of two elements, x,y, of a hyperring H is, in general, not an element but a subset of H. When the non-zero elements of a hyperring form a multiplicative group, the hyperring is called a hyperfield, and this structure generalizes that of a field. A certain class of hyperfields (residual hyperfields of valued fields) has been used by the author [1] as an important technical tool in his theory of approximation of complete valued fields by sequences of such fields. Tne non-commutative theory of hyperrings (particularly Artinian) has been studied in depth by Stratigopoulos [2].http://dx.doi.org/10.1155/S0161171283000265hyperringhyperfield. |
| spellingShingle | Marc Krasner A class of hyperrings and hyperfields International Journal of Mathematics and Mathematical Sciences hyperring hyperfield. |
| title | A class of hyperrings and hyperfields |
| title_full | A class of hyperrings and hyperfields |
| title_fullStr | A class of hyperrings and hyperfields |
| title_full_unstemmed | A class of hyperrings and hyperfields |
| title_short | A class of hyperrings and hyperfields |
| title_sort | class of hyperrings and hyperfields |
| topic | hyperring hyperfield. |
| url | http://dx.doi.org/10.1155/S0161171283000265 |
| work_keys_str_mv | AT marckrasner aclassofhyperringsandhyperfields AT marckrasner classofhyperringsandhyperfields |