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Wednesday, July 22, 2020 | History

6 edition of Quasi-ideals in rings and semigroups found in the catalog.

Quasi-ideals in rings and semigroups

by OttoМЃ Steinfeld

  • 293 Want to read
  • 22 Currently reading

Published by Akadémiai Kiadó in Budapest .
Written in English

    Subjects:
  • Associative rings.,
  • Semigroups.,
  • Ideals (Algebra)

  • Edition Notes

    StatementOttó Steinfeld.
    SeriesDisquisitiones mathematicae Hungaricae ;, 10
    Classifications
    LC ClassificationsQA251.5 .S79
    The Physical Object
    Paginationxi, 154 p. ;
    Number of Pages154
    ID Numbers
    Open LibraryOL4480299M
    ISBN 109630516969
    LC Control Number79308570

    Kuroki (Kuroki, ) initiated the notion fuzzy ideals, bi-ideals, quasi-ideals of semigroups. The book by Mordeson (Mordeson, Malik & Kuroki, ), deals with the theory of fuzzy semigroups and their use in fuzzy coding, fuzzy finite state machines and fuzzy languages. Ideals theory in semigroups, like all other algebraic structures, play an important role in studying them. Steinfeld gave the idea of quasi ideals in rings and semigroups respectively in his articles [12] and [11]. Iseki [5] developed this concept for semirings having no zero and studied important characterizations of semirings using quasi ideals.

      O. Steinfeld, Quasi ideals in Rings and Semigroups, Akademiaikiado, Budapest, A.D. Wallace, Relative ideals in semigroups I, Colloq. Math. 9, 55–61, In Dixit and Dewan studied about the quasi-ideals in ternary semigroups. are generalization of right ideals, lateral ideals and left ideals. In S. Kar introduced the notion of quasi-ideal and.

      The characterization of regular rings, semigroups or ordered semigroups in terms of right ideals and left ideals is well known,,. The characterization of regular le-semigroups in terms of right ideal elements and left ideal elements is known as well. In this paragraph we give the analogous result by means of fuzzy sets. of bi-ideals in rings and semigroups were introduced by Lajos and Szasz [11]. In , Steinfeld [47] rst introduced the notion of quasi ideals for semigroups and then for rings. Iseki [4, 5, 6] introduced the concept of quasi ideal for a semiring. Henriksen [3] studied ideals in semirings. Quasi ideals in semirings studied by Jagtap and Pawar.


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Quasi-ideals in rings and semigroups by OttoМЃ Steinfeld Download PDF EPUB FB2

Quasi-ideals in rings and semigroups. Budapest: Akadémiai Kiadó, (OCoLC) Material Type: Internet resource: Document Type: Book. Immediate online access to all issues from Subscription will auto renew annually.

In this paper, some intersection properties and characterizations of (m,n) quasi-ideals of semigroups are taken into account. We also obtain some results for left ideals, right ideals and.

Quasi-ideals in rings and semigroups O. Steinfeld. Semigroup forum () Volume: 19, page ; ISSN: ; /e; Access Full Article top Access to full text. How to cite top. Characterizations of Ordered Semigroups by New Type of Interval Valued Fuzzy Quasi-Ideals Tang, Jian, Xie, Xiangyun, and Luo, Yanfeng, Journal of Applied Mathematics, ; Review: Robert Gilmer, Commutative semigroup rings Ohm, Jack, Bulletin (New Series) of.

In this paper, we study the concept of minimal quasi-ideals in ternary semiring and prove some standard results analogous to ring theory. We also introduced the concept of a \(Q\)-simple ternary semiring and \(0\)-\(Q\)-simple ternary semiring and characterize \(0\)-minimal quasi-ideals in terms of \(Q\)-simple ternary semiring.

*immediately available upon purchase as print book shipments may be delayed due to the COVID crisis. ebook access is temporary and does not include ownership of the ebook. Only valid for books with an ebook version.

Springer Reference Works are not included. This book, along with volume I, which appeared previously, presents a survey of the structure and representation theory of semi groups. Volume II goes more deeply than was possible in volume I into the theories of minimal ideals in a semi group, inverse semi groups, simple semi groups, congruences on a semi group, and the embedding of a semi group in a by: Steinfeld surveyed widely the generalization for the notion of quasi-ideal in rings and semigroups in Dixit and Dewan studied about the quasi-ideals and bi-ideals of ternary semigroups.

The notion of quasi-ideals was flrst introduced by O. Steinfeld and for rings and semigroups, respectively.

We mean by a quasi-ideal on a semigroupSis a subsemigroupQof (S;+) satisfyingSQ\QS µ Q. Kiyoshi Iseki introduced this concept for semirings without zero and proved some results. Abstract Several statements on quasi-ideals of semirings are given in this paper, where these semirings may have an absorbing element O or not.

In Section 2 we characterize regular semirings and regular elements of semi-rings using quasi-ideals (cf. Thms.and ). In Section 3 we deal with (O −) minimal and canonical quasi-ideals. The aim of this note is to use some structural properties of quasi-commutative semigroups to get information on their ideals.

This is a preview of subscription content, log in. Keywords: Γ-semirings, quasi-ideals, regular Γ-semirings 1 Introduction The notions of quasi-ideals for rings and semigroups were introduced by O. Steinfeld in [13] and [14], respectively.

We can see general properties of quasi-ideals for rings and semigroups in [15]. The notion of a Γ-semigroup was introduced by M. Sen in [10].

The notions of quasi-ideals of rings and semigroups were introduced by Steinfeld in andrespectively. The notion of Γ-semigroups was introduced by Sen in Γ-semigroups generalize semigroups.

Many classical notions of semigroups were extended to Γ-semigroups. In this paper, we study some properties of minimal quasi-ideals in Γ. Quasi-ideal was first introduced by O. Steinfeld for semigroups and then for rings by the same author O. Steinfeld where it is seen that quasi-ideal is a generalization of left and right ideals.

Kiyoshi Iseki introduced quasi-ideals for semirings without zero and showed results based on them. Keywords: Γ-semirings, quasi-ideals 1 Introduction and Preliminaries The notions of quasi-ideals have been introduced by O. Steinfeld [12] and [13] for rings and semigroups, respectively (See [14] for general properties of quasi-ideals for rings and semigroups).

The notion of a Γ-semigroup have been [9]theyear The notion of quasi-ideals play an important role in the study of ring theory, semiring theory, semigroup theory and ordered semigroup theory etc. for a detail study of quasi-ideals in rings and. BRAJA ISLAM, ; JAGATAP and PAWAR studied about quasi ideals in Γ-semirings.

CHINRAM studied about quasi-ideals and obtained some characterizations of regular Γ-semigroups. CHINRAM and SIAMMAI generalized the green’s relations in semigroups. Group membership in rings and semigroups. Losey, Gerald and Schneider, Hans, Pacific Journal of Mathematics, ; On the adjoint semigroups of rings, I Szász, Ferenc, Proceedings of the Japan Academy, ; On semigroups, semirings, and rings of quotients Smith, David A., Journal of Science of the Hiroshima University, Series A-I (Mathematics.

The concept of non-k-quasi-coincidence of an interval valued ordered fuzzy point with an interval valued fuzzy set is fact, this concept is a generalized concept of the non-k-quasi-coincidence of a fuzzy point with a fuzzy using this new concept, we introduce the notion of interval valued (∈ ¯, ∈ ¯ ∨ q k ~ ¯)-fuzzy quasi-ideals of ordered semigroups and study.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): The notions of quasi-ideals of rings and semigroups were introduced by Steinfeld in andrespectively.

The notion of Γ-semigroups was introduced by Sen in What is this book about Analyzing proofs of results about various algebraic objects (groups, semigroups, rings), it is easy to notice two types of results: syntactic results involving words, automata, languages, and semantic results involving algebraic properties of subalgebras and homo.A ring R is defined to be nil-semicommutative if ab∈N(R) implies arb∈N(R) for a,b,r∈R, where N(R) stands for the set of nilpotents of R.

Nil-semicommutative rings are generalization of NI rings.