scholarly journals EQUATIONS OVER DIRECT POWERS OF ALGEBRAIC STRUCTURES IN RELATIONAL LANGUAGES

2021 ◽  
pp. 5-11
Author(s):  
A. Shevlyakov ◽  
◽  
Keyword(s):  
Algebraic Structure ◽  
Rectangular Band ◽  
Finite Semigroup ◽  
Minimal Ideal ◽  
Algebraic Structures ◽  
Direct Power

For a semigroup S (group G) we study relational equations and describe all semigroups S with equationally Noetherian direct powers. It follows that any group G has equationally Noetherian direct powers if we consider G as an algebraic structure of a certain relational language. Further we specify the results as follows: if a direct power of a finite semigroup S is equationally Noetherian, then the minimal ideal Ker(S) of S is a rectangular band of groups and Ker(S) coincides with the set of all reducible elements

Boolean powers of groups

1982 ◽  
Vol 91 (3) ◽  
pp. 375-396 ◽  
Author(s):  
A. B. Apps
Keyword(s):  
Finite Groups ◽  
Algebraic Structure ◽  
Boolean Ring ◽  
Direct Power ◽  
Boolean Power ◽  
Boolean Extension

If M is any algebraic structure, and R is any Boolean ring, then a structure called the (bounded) Boolean power of M by R, denoted MR, can be defined. This construction, which is also called a bounded Boolean extension, is a sort of generalized direct power, and was introduced by Foster in the 1950's (as a refinement of his previous notion of a Boolean extension). In this paper we shall study isomorphism types and automorphisms of Boolean powers of groups, and obtain information about their characteristic subgroups: we shall be chiefly concerned with Boolean powers of finite groups.

On single valued neutrosophic sets and neutrosophic א-structures: Applications on algebraic structures (hyperstructures)

2020 ◽  
pp. 108-117
Author(s):  
Madeleine Al Al-Tahan ◽  
◽  
◽  
Bijan Davvaz
Keyword(s):  
Algebraic Structure ◽  
Algebraic Structures ◽  
Neutrosophic Sets

In this paper, we find a relationship between SVNS and neutrosophic N-structures and study it. Moreover, we apply our results to algebraic structures (hyperstructures) and prove that the results on neutrosophic N-substructure (subhyperstructure) of a given algebraic structure (hyperstructure) can be deduced from single valued neutrosophic algebraic structure (hyperstructure) and vice versa.

An approach to fuzzy multi-ideals of near rings

2021 ◽  
pp. 1-11
Author(s):  
Madeline Al Tahan ◽  
Sarka Hoskova-Mayerova ◽  
Bijan Davvaz
Keyword(s):  
Algebraic Structure ◽  
Algebraic Structures

In recent years, fuzzy multisets have become a subject of great interest for researchers and have been widely applied to algebraic structures including groups, rings, and many other algebraic structures. In this paper, we introduce the algebraic structure of fuzzy multisets as fuzzy multi-subnear rings (multi-ideals) of near rings. In this regard, we define different operations on fuzzy multi-ideals of near rings and we generalize some results known for fuzzy ideals of near rings to fuzzy multi-ideals of near rings.

scholarly journals Logic and Truth: Some Logics without Theorems

2008 ◽  
pp. 104-117
Author(s):  
Jayanta Sen ◽  
Mihir Kumar Chakraborty
Keyword(s):  
Algebraic Structure ◽  
Logical Consequence ◽  
The Other ◽  
Algebraic Structures ◽  
Sequent Calculi

Two types of logical consequence are compared: one, with respect to matrix and designated elements and the other with respect to ordering in a suitable algebraic structure. Particular emphasis is laid on algebraic structures in which there is no top-element relative to the ordering. The significance of this special condition is discussed. Sequent calculi for a number of such structures are developed. As a consequence it is re-established that the notion of truth as such, not to speak of tautologies, is inessential in order to define validity of an argument.

scholarly journals On products of all elements of a finite semigroup

1999 ◽  
Vol 42 (3) ◽  
pp. 551-557 ◽  
Author(s):  
P. Z. Hermann ◽  
E. F. Robertson ◽  
N. Ruškuc
Keyword(s):  
Maximal Subgroup ◽  
Finite Semigroup ◽  
Minimal Ideal

Let S be a finite semigroup. Consider the set p(S) of all elements of S which can be represented as a product of all the elements of S in some order. It is shown that p(S) is contained in the minimal ideal M of S and intersects each maximal subgroup H of M in essentially the same way. The main result shows that p(S) intersects H in a union of cosets of H′.

scholarly journals Growth sequences of finite semigroups

1987 ◽  
Vol 43 (1) ◽  
pp. 16-20 ◽  
Author(s):  
James Wiegold ◽  
H. Lausch
Keyword(s):  
Real Number ◽  
Finite Semigroup ◽  
Piecewise Linear ◽  
The Other ◽  
Direct Power ◽  
Growth Sequence ◽  
Group Of Units ◽  
Number Of Generators ◽  
Finite Semigroups ◽  
Minimum Number

AbstractThe growth sequence of a finite semigroup S is the sequence {d(Sn)}, where Sn is the nth direct power of S and d stands for minimum generating number. When S has an identity, d(Sn) = d(Tn) + kn for all n, where T is the group of units and k is the minimum number of generators of S mod T. Thus d(Sn) is essentially known since d(Tn) is (see reference 4), and indeed d(Sn) is then eventually piecewise linear. On the other hand, if S has no identity, there exists a real number c > 1 such that d(Sn) ≥ cn for all n ≥ 2.

scholarly journals The subpower membership problem for semigroups

2016 ◽  
Vol 26 (07) ◽  
pp. 1435-1451 ◽  
Author(s):  
Andrei Bulatov ◽  
Marcin Kozik ◽  
Peter Mayr ◽  
Markus Steindl
Keyword(s):  
Finite Semigroup ◽  
Transformation Semigroup ◽  
Membership Problem ◽  
Clifford Semigroup ◽  
Direct Power ◽  
Nilpotent Semigroup ◽  
Full Transformation ◽  
Commutative Semigroups ◽  
Np Complete ◽  
A Finite Group

Fix a finite semigroup [Formula: see text] and let [Formula: see text] be tuples in a direct power [Formula: see text]. The subpower membership problem (SMP) asks whether [Formula: see text] can be generated by [Formula: see text]. If [Formula: see text] is a finite group, then there is a folklore algorithm that decides this problem in time polynomial in [Formula: see text]. For semigroups this problem always lies in PSPACE. We show that the [Formula: see text] for a full transformation semigroup on [Formula: see text] or more letters is actually PSPACE-complete, while on [Formula: see text] letters it is in P. For commutative semigroups, we provide a dichotomy result: if a commutative semigroup [Formula: see text] embeds into a direct product of a Clifford semigroup and a nilpotent semigroup, then [Formula: see text] is in P; otherwise it is NP-complete.

Algebraic Structure of Step Traces and Interval Traces

2020 ◽  
Vol 175 (1-4) ◽  
pp. 253-280
Author(s):  
Ryszard Janicki ◽  
Łukasz Mikulski
Keyword(s):  
Algebraic Structure ◽  
Formal Analysis ◽  
Concurrent Systems ◽  
Interval Order ◽  
Canonical Forms ◽  
Algebraic Structures ◽  
Main Subject

Traces and their extensions as comtraces, step traces and interval traces are quotient monoids over sequences or step sequences that play an important role in the formal analysis and verification of concurrent systems. Step traces are generalizations of comtraces and classical traces while interval traces are specialized traces that can deal with interval order semantics. The algebraic structures and their properties as projections, hidings, canonical forms and other invariants are very well established for traces and fairly well established for comtraces. For step traces and interval traces they are the main subject of this paper.

Some Subfields of Qp, and their Non-Standard Analogues

1974 ◽  
Vol 26 (02) ◽  
pp. 473-491
Author(s):  
Diana L. Dubrovsky
Keyword(s):  
Algebraic Structure ◽  
Recursion Theory ◽  
Algebraic Structures ◽  
Mathematical Structures ◽  
Closed Fields ◽  
Standard Models ◽  
Algebraically Closed Fields

The desire to study constructive properties of given mathematical structures goes back many years; we can perhaps mention L. Kronecker and B. L. van der Waerden, two pioneers in this field. With the development of recursion theory it was possible to make precise the notion of "effectively carrying out" the operations in a given algebraic structure. Thus, A. Frölich and J. C. Shepherdson [7] and M. O . Rabin [13] studied computable algebraic structures, i.e. structures whose operations can be viewed as recursive number theoretic relations. A. Robinson [18] and E. W. Madison [11] used the concepts of computable and arithmetically definable structures in order to establish the existence of what can be called non-standard analogues (in a sense that will be specified later) of certain subfields of R and C, the standard models for the theories of real closed and algebraically closed fields respectively.

AN ALGEBRAIC STRUCTURE OF ZERO CURVATURE REPRESENTATIONS ASSOCIATED WITH COUPLED INTEGRABLE COUPLINGS AND APPLICATIONS TO τ-SYMMETRY ALGEBRAS

2011 ◽  
Vol 25 (23n24) ◽  
pp. 3237-3252 ◽  
Author(s):  
LIN LUO ◽  
WEN-XIU MA ◽  
ENGUI FAN
Keyword(s):  
Lie Algebras ◽  
Algebraic Structure ◽  
Algebraic Structures ◽  
Direct Sums ◽  
Zero Curvature ◽  
Integrable Couplings ◽  
Symmetry Algebras

We establish an algebraic structure for zero curvature representations of coupled integrable couplings. The adopted zero curvature representations are associated with Lie algebras possessing two sub-Lie algebras in form of semi-direct sums of Lie algebras. By applying the presented algebraic structures to the AKNS systems, we give an approach for generating τ-symmetry algebras of coupled integrable couplings.

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