Over the past 25 years, I have been immersed in research in Algebra and more particularly in ring theory. I embarked on writing this book on Smarandache rings (Srings) specially to motivate both ring theorists and Smarandache algebraists to develop and study several important and innovative properties about S-rings

Vasantha, Kandasamy

English

ZENODO

A characterization of f-ring without non-zero nilpotents,

A colour Problem for infinite graphs and a problem in theory of relations,

a composite number}; Can we have P=G ∪ V?

A generalization of strongly regular rings,

A note on additive subgroups of finite rings,

A note on f-group rings without non-zero nilpotents,

A note on F-rings,

A note on group rings which are F-rings,

A note on pre J-group rings,

A note on semi idempotents in group rings,

A note on semigroup rings which are Boolean rings,

A note on semigroup rings which are pre prings,

A note on the mod p-envelope of a cyclic group,

A note on the modular group ring of finite pgroup,

A note on the modular group ring of the symmetric group Sn,

A note on the modular semigroup ring of a finite idempotent semigroup,

A note on units and semi idempotents elements in commutative group rings,

A Radical Approach to Algebra,

A representation of generalized Boolean Rings,

A Structure theorem for generalized J rings,

A theorem on normal semigroups,

and Suenago Takashi, Generalizations of von Neuman regular rings and n-like rings,

Artinian Modules over a matrix ring, Infinite length modules,

be a group ring; obtain a necessary and sufficient condition so that the group ring RG is a generalized Hamiltonian ring.

be the group ring of the torsion free non-abelian group G and K the field of characteristic 0. Can KG be a a. ZI ring? b. S-ZI ring? c. Weakly ZI ring? d. S-weakly ZI ring? e. pseudo ZI ring?

Can a torsion free non-abelian group be conditionally commutative?

Can the semigroup ring ZpS(n) have non-trivial S-super-idempotents?

Can we say by using Zp, p a prime we can construct P which is a finite division ring of dimension p4, p an odd prime?

Characterize or classify all semigroup rings ZnS(P) that are a. pseudo ZI ring.

Characterize those group rings (semigroup rings) which has fixed support subring.

Characterize those normal rings which are not S-normal rings.

Characterize those normal rings which are S-normal rings.

Characterize those S-group rings which are S-Artinian.

Characterize those S-semigroup rings which are S-Artinian.

Characterize those semigroup rings RS so that they are generalized Hamiltonian rings.

Characterize those semigroup rings which are

Characterize those semigroup rings which are a. S-subsemi ideal rings. b. subsemi ideal rings.

Chinese Quat.

Ciric Miroslov and Petkovic Tatjana, Uniformly π-regular semigroups: a survey,

Classify those group rings (semigroup rings) which are a. semi connected.

Classify those group rings (semigroup rings) which has fixed support semigroup.

Classify those group rings (semigroup rings) which have S-fixed support subring.

Classify those group rings and semigroup rings which are a. S-Hamiltonian. b. S-Hamiltonian II.

Classify those group rings which are a. normal rings. b. S-normal rings.

Classify those rings in which every S-Hamiltonian II is also S-Hamiltonian I.

Classify those rings which are a. Jk ring. b. S-Jk ring.

Classify those rings which are a. stable rings. b. S-stable rings.

Coloring of commutative rings,

Coloring of group rings,

Commutative Algebra,

Commutativity of rings inherited by the location of Herstein's condition,

Connectivity in weakly Boolean Topological rings,

Determine the class of group rings which are S-Noetherian.

Direct sum of strongly regular rings and zero rings,

Does the group ring ZpG when G is a cyclic group of order q have non-trivial super-idempotents when:

Does there exist a class of semigroup rings which are S-Noetherian? a. S-subsemiideal rings. b. subsemiideal rings.

Does there exist a ring R in which every triple x, y,

Equivalence of semigroups with systems of local units,

Exchange rings having stable range one,

Extensions of clean rings,

f-semigroup rings,

Filial semigroups and semigroup rings,

Find conditions on the ring R to have the S-ideals I and S-ideals II to be modular.

Find conditions on the ring so that all S-ideals II are S-subrings.

Find conditions on the ring so that every S-Jk-ring is a Jk ring and every Jk ring is a S-Jk-ring.

Find Smarandache analogue of classical theorems in ring theory.

Find those S-rings whose S-subrings forms a quasi distributive lattice.

Finite rings which has isomorphic quotient rings formed by non-maximal ideals,

Finite zeros and finite zero-divisors,

Give a necessary and sufficient condition for the group ring to be a. S-subsemi ideal rings. b. subsemi ideal rings

given in problem 100 to define some interesting and innovative Smarandache notions on rings.

Group rings which are a direct sum of subrings,

Group rings which have trivial subrings,

Group rings which satisfy super ore condition,

Guassian ideals and the Dedekind- Merlens lemma,

have idempotents other than the ones given in Zn?

Higher level orders on non-commutative rings,

Hypergroups (Zq , q),

Ideal theory,

Idempotents in the group ring of a cyclic group,

Infinite Group Rings, Pure and Appl.

Inner associative rings,

Inner Zero Square ring,

Introduction to Commutative Algebra,

is a conditionally commutative group and R a conditionally commutative ring. Can the group ring RG be a conditionally commutative ring?

Lie ideals of Z2S3,

Modules whose lattice of submodules is distributive,

Modules with a group of operators,

Monic and Monic free ideals in a polynomial semiring,

n-ideal rings,

Nil generalized Hamiltonian rings, Heilongiang Daxue Ziran Kexue Xuebao,

Note on integral closure of semigroups,

Obedient ideals in a finite ring,

Obtain conditions on a ring R so that every subsemi ideal ring is a S-subsemi ideal.

Obtain conditions on the group G and on the ring R so that the group ring RG has non-trivial super idempotents.

Smarandache rings

Abstract

Similar works

Full text

Available Versions

ZENODO