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The First Isomorphism Theorem and Other Properties of Rings

100%

Korniłowicz A. , Schwarzweller C.

Formalized Mathematics

2014

tom 22

nr 4

291-301

Different properties of rings and fields are discussed [12], [41] and [17]. We introduce ring homomorphisms, their kernels and images, and prove the First Isomorphism Theorem, namely that for a homomorphism f : R → S we have R/ker(f) ≅ Im(f). Then we define prime and irreducible elements and show that every principal ideal domain is factorial. Finally we show that polynomial rings over fields are Euclidean and hence also factorial

A New Approach for the Reconstruction of Object-Based Images in Discrete Tomography

75%

Brocchi S.

Fundamenta Informaticae

2014

tom Vol. 135, nr 1/2

43--57

In this paper we tackle the problem of the reconstruction of object based images, specifically formed by a set of circles inside a ring. By analyzing the projections of the image, we are able to determine some coordinates corresponding to interest points that give significant information about features of the image of aid in the reconstruction. Our approach yields promising results in comparison to other methods in literature. Finally, we discuss how a similar approach could be extended to more complex problems deriving from tomographic applications, in order to develop an efficient method exploiting the prior knowledge assumed on an image.

Some results on 2-absorbing ideals in commutative semirings

51%

Kumar P. , Dubey M. K. , Sarohe P.

Journal of Mathematics and Applications

2015

tom Vol. 38

77--84

In this paper, we study the concepts of 2-absorbing and weakly 2-absorbing ideals in a commutative semiring with non-zero identity which is a generalization of prime ideals of a commutative semiring and prove number of results related to the same. We also use these concepts to prove some results of Q-ideals in terms of subtractive extension of ideals in a commutative semiring.