Semimodules over a-regular semirings
Mohamed Elsayed Abdel-aal;
Abstract
Abstract
Abstract
In this thesis, we study the notions of regularity (in the sense of Von Neumann), k-regularity and complete k-regularity for semirings. On the other side, we study the notions of injectivity and P-injectivity for semimodules. In fact, for any cardinal, 2::; a::; 0 , we introduce the notions of a-regular semirings and a-injective semimodules. In particular, if a = 2, these notions coincide, respectively, with Von Neumann regularity for semirings and P-injectivety for semimodules. Characterizations of a-regular semirings are given and several invariant properties are examined. Indeed, we prove that a semiring R is a-regular if and only if every left R-semimodule is
a-injective. Regular semirings with central idempotents are investigated and shown to admit an involution. Finally, consistent a-systems of equations are studied and applied to obtain a characterization of a-injective cancellative semimodules over cancellative semirings
2000 Mathematic Subject Classification : 16Y60
Keywords : a-regular semirings, k-regular semirings, a-injective semimodules, a-systems of equations.
1
Abstract
In this thesis, we study the notions of regularity (in the sense of Von Neumann), k-regularity and complete k-regularity for semirings. On the other side, we study the notions of injectivity and P-injectivity for semimodules. In fact, for any cardinal, 2::; a::; 0 , we introduce the notions of a-regular semirings and a-injective semimodules. In particular, if a = 2, these notions coincide, respectively, with Von Neumann regularity for semirings and P-injectivety for semimodules. Characterizations of a-regular semirings are given and several invariant properties are examined. Indeed, we prove that a semiring R is a-regular if and only if every left R-semimodule is
a-injective. Regular semirings with central idempotents are investigated and shown to admit an involution. Finally, consistent a-systems of equations are studied and applied to obtain a characterization of a-injective cancellative semimodules over cancellative semirings
2000 Mathematic Subject Classification : 16Y60
Keywords : a-regular semirings, k-regular semirings, a-injective semimodules, a-systems of equations.
1
Other data
| Title | Semimodules over a-regular semirings | Other Titles | اشباه التشكيلات المبنيه على اشباه الحلقات a- النظاميه | Authors | Mohamed Elsayed Abdel-aal | Issue Date | 2005 |
Recommend this item
Similar Items from Core Recommender Database
Items in Ain Shams Scholar are protected by copyright, with all rights reserved, unless otherwise indicated.