On perfect ideals of seminearrings
- PDF / 367,732 Bytes
- 20 Pages / 439.37 x 666.142 pts Page_size
- 75 Downloads / 258 Views
On perfect ideals of seminearrings Kavitha Koppula1 · Babushri Srinivas Kedukodi1
· Syam Prasad Kuncham1
Received: 31 May 2020 / Accepted: 24 September 2020 © The Managing Editors 2020
Abstract In this paper, we present the notion of perfect ideal of a seminearring S and prove that the kernel of a seminearring homomorphism is a perfect ideal. We show that the quotient structure S/I is isomorphic to the structure ST (I ) . Finally, we prove isomorphism theorems in seminearrings by using tame condition. Keywords Seminearring · Perfect ideal · Tame condition · Isomorphism theorems Mathematics Subject Classification 16Y30 · 16Y60
1 Introduction The concept seminearring is introduced by Van Hoorn and Van Rootselaar (1967) in 1967. A right (left) seminearring S is an algebraic structure that forms a semigroup under addition (+) as well as multiplication (·) and satisfies right (left) distributive condition. A well known example of a seminearring is the set of all mappings from additive semigroup to itself under pointwise addition and composition of mappings. Van Hoorn and Van Rootselaar (1967) defined ideal of a seminearring as the kernel of a seminearring homomorphism. Later, Ahsan (1995a, b) studied specific type of ideals and proved their properties in a seminearring. Subsequently, Weinert (1982) reported results on multiplicative cancellativity in seminearrings. Jun and Kim (2002) introduced gamma seminearring as a generalization of seminearring and provided the results on prime and semiprime ideals of gamma seminearrings. Khan et al. (2019) studied the notion of weakly prime and weakly primary
B
Babushri Srinivas Kedukodi [email protected] Kavitha Koppula [email protected] Syam Prasad Kuncham [email protected]
1
Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka 576104, India
123
Beitr Algebra Geom
ideals of gamma seminearrings and provided their characterizations. The concept kideals of semirings is extended to seminearrings by Kornthorng and Iampan (2012) and obtained related results. Various results on classes of endomorphism seminearrings over Clifford and Brandt semigroups are obtained by Gilbert and Samman (2010a, b). If (S, +) is a semigroup, then (M(S), +, .) is a multiplicatively regular seminearring but not an additively regular seminearring. Results on congruences of various additively regular seminearrings are provided by Sardar and Mukherjee (2014), Mukherjee et al. (2017) and Mukherjee et al. (2019). The idea of S-semigroup giving rise to an algebraic structure of seminearring is used by Krishna and Chatterjee (2005) to establish a categorical representation, to provide a classification of seminearrings and presented approximate categories of primitive seminearrings. The structure of transformation of semigroups is studied using Eilenberg’s technique by Krishna and Chatterjee (2007) and extended the Holcombes holonomy decomposition of nearrings to seminearrings. Koppula et al. (2020) defined the s
Data Loading...
