Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

On Subtractive Ideals of (m; n)-semirings


Affiliations
1 M. J. College, Department of Mathematics, Jalgaon, India
2 Dhanaji Nana Mahavidyalaya, Department of Mathematics, Faizpur, India
     

   Subscribe/Renew Journal


Let R be a commutative (m, n)-semiring with an identity element. It is proved that every partitioning ideal of R is a subtractive ideal. Also if I is a partitioning ideal of R, then a relation between the set of subtractive ideals (subtractive prime ideals) of R containing I and the set of subtractive ideals (subtractive prime ideals) of the quotient (m, n)-semiring R/I(Q) is obtained.

Keywords

(m, n)-semiring, Subtractive ideal, Partitioning ideal, Quotient (m, n)-semiring
Subscription Login to verify subscription
User
Notifications
Font Size


  • Syed Eqbal Alam, Shrisa Rao and Bijan Davvaz, (m, n)-Semirings and a generalised fault tolerance algebra of systems, J. Appl. Math., Vol. 2013 Article ID 482391 10 pages.
  • P. J. Allen, A fundamental theorem of homomorphism for semirings, Proc. Amer. Math. Soc., 21 (1969), 412-416.
  • P. J. Allen, J. Neggers and H. S. Kim, Ideal theory in commutative A-semirings, Kyungpook Math. J.,46(2006), 261-271.
  • Shahabaddin Ebrahimi Atani, The ideal theory in quotients of commutative semirings, Glasnik mathematicki, 42 (2007), 301-307.
  • J. N. Chaudhari and K. J. Ingale, On partitioning and subtractive ideals of ternary semirings, Kyungpook Math. J., 51 (2011), 69-76.
  • G. Crombez, On (n;m)-rings, Abh. Math. Sem. Univ. Hamburg, 37 (1972), 180-199.
  • A. Pop, Remarks on Embedding Theorems of (m; n)-Semirings, Bul. Stiint. Univ. Baia Mare Ser. B, Mathematica-Informatica 16(2000), 297-302.
  • Adina Pop and M. Lauran, A Note on the Morphism theorems for (n;m)-Semirings, Creat. Math. Inform., 27 (1) (2018), 79-88.
  • Maria S. Pop and Adina Pop, Some properties of generalized semirings, Carpathian J. Math 24 No. 3(2008), 397-402.
  • Y. Zhu, On the Jacobson radical of (m,n)-semirings, Algebra 2013, Article ID 272104, 9 pages.

Abstract Views: 360

PDF Views: 0




  • On Subtractive Ideals of (m; n)-semirings

Abstract Views: 360  |  PDF Views: 0

Authors

J. N. Chaudhari
M. J. College, Department of Mathematics, Jalgaon, India
Harish Nemade
Dhanaji Nana Mahavidyalaya, Department of Mathematics, Faizpur, India

Abstract


Let R be a commutative (m, n)-semiring with an identity element. It is proved that every partitioning ideal of R is a subtractive ideal. Also if I is a partitioning ideal of R, then a relation between the set of subtractive ideals (subtractive prime ideals) of R containing I and the set of subtractive ideals (subtractive prime ideals) of the quotient (m, n)-semiring R/I(Q) is obtained.

Keywords


(m, n)-semiring, Subtractive ideal, Partitioning ideal, Quotient (m, n)-semiring

References





DOI: https://doi.org/10.18311/jims%2F2021%2F27834