Department of Mathematics: Recent submissions

  • On a field-theoretic invariant for extensions of commutative rings, II 
    Kumar, Rahul (Palestine Polytechnic University, 2021)
    This paper is a sequel. The earlier paper introduced, for any (unital) extension of (commutative unital) rings R T, an invariant L(T=R) defined as the supremum of the lengths of chains of intermediate fields in the ...
  • A note on imbedded prime divisors 
    Kumar, Rahul (Springer, 2020-06)
    In this note, we show that a part of Ratliff (Proc Am Math Soc 101(3):395–402, 1987, Remark 2.2) is not correct. Some conditions are given under which the same holds.
  • A note on ϕ -λ -rings and ϕ -Δ -rings 
    Kumar, Rahul (Springer, 2021-01)
    Let H denotes the set of all commutative rings R in which the set of all nilpotent elements, denoted by Nil(R), is a prime ideal of R and is comparable to every ideal of R. Let R∈H be a ring and T(R) be its total quotient ...
  • A note on residually small rings and modules 
    Kumar, Rahul (Palestine Polytechnic University, 2022)
    In this note, how the residual smallness of R(+)M is related to the residual smallness of the ring R and the R-module M is discussed.
  • Maximal non-ϕ-pseudo-valuation rings 
    Kumar, Rahul (World Scientific, 2022)
    The notion of maximal non-ϕ-pseudo-valuation ring is introduced which generalizes the concept of maximal non-pseudo-valuation domain. The equivalence of maximal non-ϕ-PVR and maximal non-local ring is established under ...
  • A question about maximal non ϕ -chained subrings 
    Kumar, Rahul (The Korean Mathematical Society., 2023-01)
    Let H0 be the set of rings R such that Nil(R)=Z(R) is a divided prime ideal of R. The concept of maximal non ϕ-chained subrings is a generalization of maximal non valuation subrings from domains to rings in H0. This ...
  • A note on maximal non-λ -rings 
    Kumar, Rahul (World Scientific, 2023)
    Let H0 denote the set of all rings R such that Nil(R) is a divided prime ideal with Nil(R)=Z(R). We study the concept of maximal non-λ-rings in class H0 and generalize the results of maximal non-λ-domains.
  • A Corrigendum to “Hereditary Properties Between a Ring and Its Maximal Subrings” 
    Kumar, Rahul (Springer, 2018-11)
    Let R be a commutative ring with identity. In A. Azarang, O. A. S. Karamzadeh, and A. Namazi, [Ukr. Math. J., 65, No. 7, 981–994 (2013) (Proposition 3.1)], it was proved that if R is an integral domain and S is a maximal ...
  • Maximal non λ-subrings 
    Kumar, Rahul (Springer, 2020)
    Let R be a commutative ring with unity. The notion of maximal non -subrings is introduced and studied. A ring R is called a maximal non -subring of a ring T if R T is not a -extension, and for any ring S such that ...
  • A note on -domains and -domains 
    Kumar, Rahul (The Belgian Mathematical Society, 2020)
    Let R be an integral domain. Then R is said to be a λ-domain if the set of all overrings of R is linearly ordered by inclusion. If R1+R2 is an overring of R for each pair of overrings R1,R2 of R, then R is said to be a ...
  • Maximal non-Prüfer and maximal non--Prüfer rings 
    Kumar, Rahul (Taylor & Francis, 2021-10)
    Let R be a commutative ring with unity. Let H denotes the set of all rings R such that Nil(R) is a divided prime ideal. The notion of maximal non-Prüfer ring and maximal non-ϕ-Prüfer ring is introduced which generalize the ...
  • Chiral Metafilms and Surface Enhanced Raman Scattering for Enantiomeric Discrimination of Helicoid Nanoparticles 
    Kumar, Rahul (Wiley, 2023)
    Chiral nanophotonic platforms provide a means of creating near fields with both enhanced asymmetric properties and intensities. They can be exploited for optical measurements that allow enantiomeric discrimination at ...
  • λ-rings, Φ-λ-rings, and Φ-Δ-rings 
    Kumar, Rahul (FSM, 2019)
    Let R be a commutative ring with unity. The notion of λ-rings, Φ-λ-rings, and Φ-Δ-rings is introduced which generalize the concept of λ-domains and Δ-domains. A ring R is said to be a λ-ring if the set of all overrings of ...
  • A note on pairs of rings with the same prime ideals 
    Kumar, Rahul (Hiroshima University, 2022-03)
    We study the ring extensions R⊆T having the same set of prime ideals provided Nil(R) is a divided prime ideal. Some conditions are given under which no such T exists properly containing R. Using idealization theory, the ...
  • Δ -Extension of rings and invariance properties of ring extension under group action 
    Kumar, Rahul (World Scientific, 2018)
    Let R,T be commutative rings with identity such that R⊆T. A ring extension R⊆T is called a Δ-extension of rings if R1+R2 is a subring of T for each pair of subrings R1,R2 of T containing R. In this paper, a characterization ...
  • Maximal Non ϕ -Chained Rings and Maximal Non Chained Rings 
    Kumar, Rahul (Springer, 2019-06)
    Let R be a commutative ring with unity. The notion of maximal non chained subrings of a ring and maximal non ϕ-chained subrings of a ring is introduced which generalizes the concept of maximal non valuation subrings of a ...
  • On λ -extensions of commutative rings 
    Kumar, Rahul (World Scientific, 2018)
    Let R,T be commutative rings with identity such that R⊆T. We recall that R⊆T is called a λ-extension of rings if the set of all subrings of T containing R (the “intermediate rings”) is linearly ordered under inclusion. In ...
  • Number of representations of integers by binary Forms 
    Sharma, Divyum (TIFR, 2014)
    We give improved upper bounds for the number of solutions of the Thue equation F(x; y) = h where F is an irreducible binary form of degree 3:
  • Arithmetic nature of some in nite series and integrals 
    Sharma, Divyum (TIFR, 2015)
    We give an overview of some results on the transcendence nature of the sums of some in nite series. We also give some new results on the transcendence nature of some series involving mildly non-periodic functions and ...
  • Simultaneous rational approximation via Rickert’s integrals 
    Sharma, Divyum (Elsevier, 2015-01)
    Using Rickert’s contour integrals, we give effective lower bounds for simultaneous rational approximations to numbers in the sets Here are integers, is a rational number and at least one of the radicals is irrational in ...

Search DSpace


Advanced Search

Browse

My Account