Commutative rings with homomorphic power functions
A (commutative) ring R (with identity) is called m-linear (for an integer m≥2) if (a+b)m=am+bm for all a and b in R. The m-linear reduced rings are characterized, with special attention to the finite case. A structure theorem reduces the study of m-linearity to the case of prime characteristic, for...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1992-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171292000103 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850162505308962816 |
|---|---|
| author | David E. Dobbs John O. Kiltinen Bobby J. Orndorff |
| author_facet | David E. Dobbs John O. Kiltinen Bobby J. Orndorff |
| author_sort | David E. Dobbs |
| collection | DOAJ |
| description | A (commutative) ring R (with identity) is called m-linear (for an integer m≥2) if (a+b)m=am+bm for all a and b in R. The m-linear reduced rings are characterized, with special attention to the finite case. A structure theorem reduces the study of m-linearity to the case of prime characteristic, for which the following result establishes an analogy with finite fields. For each prime p and integer m≥2 which is not a power of p, there exists an integer s≥m such that, for each ring R of characteristic p, R is m-linear if and only if rm=rps for each r in R. Additional results and examples are given. |
| format | Article |
| id | doaj-art-fe535070b9cc4a0b893a6d3eb8e230b2 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1992-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-fe535070b9cc4a0b893a6d3eb8e230b22025-08-20T02:22:33ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251992-01-011519110210.1155/S0161171292000103Commutative rings with homomorphic power functionsDavid E. Dobbs0John O. Kiltinen1Bobby J. Orndorff2Department of Mathematics, University of Tennessee, Knoxville 37996-1300, TN, USADepartment of Mathematics & Comp. Sci., Northern Michigan University, Marquette 49855-5340, MI, USADepartment of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg 24061-0106, VA, USAA (commutative) ring R (with identity) is called m-linear (for an integer m≥2) if (a+b)m=am+bm for all a and b in R. The m-linear reduced rings are characterized, with special attention to the finite case. A structure theorem reduces the study of m-linearity to the case of prime characteristic, for which the following result establishes an analogy with finite fields. For each prime p and integer m≥2 which is not a power of p, there exists an integer s≥m such that, for each ring R of characteristic p, R is m-linear if and only if rm=rps for each r in R. Additional results and examples are given.http://dx.doi.org/10.1155/S0161171292000103commutative ringm-linearcharacteristicdirect productfieldJacobson radicalreduced ring. |
| spellingShingle | David E. Dobbs John O. Kiltinen Bobby J. Orndorff Commutative rings with homomorphic power functions International Journal of Mathematics and Mathematical Sciences commutative ring m-linear characteristic direct product field Jacobson radical reduced ring. |
| title | Commutative rings with homomorphic power functions |
| title_full | Commutative rings with homomorphic power functions |
| title_fullStr | Commutative rings with homomorphic power functions |
| title_full_unstemmed | Commutative rings with homomorphic power functions |
| title_short | Commutative rings with homomorphic power functions |
| title_sort | commutative rings with homomorphic power functions |
| topic | commutative ring m-linear characteristic direct product field Jacobson radical reduced ring. |
| url | http://dx.doi.org/10.1155/S0161171292000103 |
| work_keys_str_mv | AT davidedobbs commutativeringswithhomomorphicpowerfunctions AT johnokiltinen commutativeringswithhomomorphicpowerfunctions AT bobbyjorndorff commutativeringswithhomomorphicpowerfunctions |