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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

Let F(X,Y) be an irreducible binary cubic form with integer coefficients and positive discriminant D. Let k be a positive integer satisfying k < ( ( 3 D ) 1 / 4 ) / 2 π . We give improved upper bounds for the number of ...

Let F(X, Y ) = s i=0 ai Xri Yr−ri ∈ Z[X, Y ] be a form of degree r = rs ≥ 3, irreducible over Q and having at most s + 1 non-zero coefficients. Mueller and Schmidt showed that the number of solutions of the Thue ...

Following a method originally due to Siegel, we establish upper bounds for the number of primitive integer solutions to inequalities of the shape 0<|F(x,y)|≤h, where F(x,y)=(αx+βy)r−(γx+δy)r∈Z[x,y], α, β, γ and δ are ...

Nora and Wanda are two players who choose coefficients of a degree-d polynomial from some fixed unital commutative ring R. Wanda is declared the winner if the polynomial has a root in the ring of fractions of R and Nora ...