Using the tools of reverse mathematics in second-order arithmetic, as developed by Friedman, Simpson, and others, we determine the axioms necessary to develop various topics in commutative ring theory. Our main contributions to the field are as follows. We look at fundamental results concerning primary ideals and the radical of an ideal, concepts previously unstudied in reverse mathematics. Then we turn to a fine-grained analysis of four different definitions of Noetherian in the weak base system RCA_0 + Sigma-2 induction. Finally, we begin a systematic study of various types of integral domains: PIDs, UFDs and Bézout and GCD domains.</p
Let N be a near-ring, and σ be an automorphisms of N. An additive mapping d from a near-ring N into ...
In this paper, we introduce a new concept called left (right) g-MP inverse in a *-monoid. The relati...
In this paper, we use the Drazin inverse to derive some new equivalences of the reverse order law fo...
Reverse Mathematics seeks to find the minimal set existence or comprehension axioms needed to prove ...
In this paper some results concerning to right reverse derivations on prime rings with char ≠ 2 are ...
summary:Let $R$ be a prime ring with center $Z(R)$ and $I$ a nonzero right ideal of $R$. Suppose tha...
This thesis will be an introduction to commutative ring theory, with an end goal of introducing comp...
The notion of reverse derivation is studied and some properties are obtained. It is shown that in th...
Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theore...
This book provides an introduction to the basics and recent developments of commutative algebra. A g...
This book presents reverse mathematics to a general mathematical audience for the first time. Revers...
AbstractWe study the Moore–Penrose inverse (MP-inverse) in the setting of rings with involution. The...
This thesis establishes new results concerning the proof-theoretic strength of two classic theorems...
AbstractWe relate ideals in commutative rings which are products of primary ideals to ideals with pr...
This thesis establishes new results concerning the proof-theoretic strength of two classic theorems ...
Let N be a near-ring, and σ be an automorphisms of N. An additive mapping d from a near-ring N into ...
In this paper, we introduce a new concept called left (right) g-MP inverse in a *-monoid. The relati...
In this paper, we use the Drazin inverse to derive some new equivalences of the reverse order law fo...
Reverse Mathematics seeks to find the minimal set existence or comprehension axioms needed to prove ...
In this paper some results concerning to right reverse derivations on prime rings with char ≠ 2 are ...
summary:Let $R$ be a prime ring with center $Z(R)$ and $I$ a nonzero right ideal of $R$. Suppose tha...
This thesis will be an introduction to commutative ring theory, with an end goal of introducing comp...
The notion of reverse derivation is studied and some properties are obtained. It is shown that in th...
Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theore...
This book provides an introduction to the basics and recent developments of commutative algebra. A g...
This book presents reverse mathematics to a general mathematical audience for the first time. Revers...
AbstractWe study the Moore–Penrose inverse (MP-inverse) in the setting of rings with involution. The...
This thesis establishes new results concerning the proof-theoretic strength of two classic theorems...
AbstractWe relate ideals in commutative rings which are products of primary ideals to ideals with pr...
This thesis establishes new results concerning the proof-theoretic strength of two classic theorems ...
Let N be a near-ring, and σ be an automorphisms of N. An additive mapping d from a near-ring N into ...
In this paper, we introduce a new concept called left (right) g-MP inverse in a *-monoid. The relati...
In this paper, we use the Drazin inverse to derive some new equivalences of the reverse order law fo...