Related Experiment Video
Updated: Apr 17, 2026
06:35
Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
Published on: February 15, 2016
8.6K
Int-soft (generalized) bi-ideals of semigroups
Young Bae Jun1, Seok-Zun Song2
1Department of Mathematics Education, Gyeongsang National University, Jinju 660-701, Republic of Korea.
Thescientificworldjournal
|February 25, 2015
Summary
This study explores integer-soft (int-soft) left and right ideals in semigroups, introducing int-soft generalized bi-ideals. It establishes characterizations and relations for these structures, including those generated by soft sets.
Area of Science:
- Abstract Algebra
- Fuzzy Set Theory
- Soft Set Theory
Background:
- Builds upon prior work on int-soft semigroups and ideals.
- Addresses limitations in existing characterizations of int-soft structures.
Purpose of the Study:
- To further investigate properties of int-soft left/right ideals.
- To introduce and define int-soft generalized bi-ideals.
- To explore relationships between int-soft generalized bi-ideals and int-soft semigroups.
Main Methods:
- Theoretical analysis of algebraic structures.
- Introduction of new concepts: int-soft generalized bi-ideals.
- Examination of characterizations and generated ideals.
Main Results:
- Further properties and characterizations of int-soft left/right ideals are established.
- The concept of int-soft generalized bi-ideals is formally introduced.
- Relations between int-soft generalized bi-ideals and int-soft semigroups are discussed.
Conclusions:
- The study provides a deeper understanding of int-soft algebraic structures.
- New characterizations for int-soft generalized bi-ideals and int-soft bi-ideals are presented.
- Methods for establishing int-soft generalized bi-ideals from soft sets are developed.
Related Concept Videos
01:30Fundamental Theorem of Algebra
455
The Fundamental Theorem of Algebra is central to the study of polynomial equations, asserting that every non-constant polynomial with complex coefficients has at least one complex zero. This means that a polynomial of degree n ≥ 1, written as: with an ≠ 0, has at least one solution in the complex number system. Since the set of real numbers is a subset of complex numbers, this theorem applies equally to polynomials with real coefficients.Building on this result, the...
455
01:16SFG Algebra
421
In Signal Flow Graph (SFG) algebra, the value a node represents is determined by the sum of all signals entering that node. This summed value is then transmitted through every branch leaving the node, making the SFG a powerful tool for visualizing and analyzing control systems.
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...
421
01:25The Intermediate Value Theorem
440
The Intermediate Value Theorem is a foundational result in calculus that guarantees the existence of solutions within certain intervals for continuous functions. Formally, the Intermediate Value Theorem states that if a function f is continuous on the closed interval [a, b], and if N is any value between f(a) and f(b), then there exists at least one c ∈ (a, b) such that f(c) = N. This theorem is instrumental in proving the existence of roots and in analyzing the behavior of continuous...
440
01:29Indeterminate Products
132
Indeterminate forms also arise in the evaluation of limits involving products, particularly when one factor approaches zero while the other tends to positive or negative infinity. This situation, commonly described as a zero-times-infinity form, does not have an immediately interpretable outcome. Depending on how the factors behave relative to one another, the limit of such a product may be zero, infinite, or a finite nonzero value.Product Limits and Algebraic RewritingTo analyze limits of this...
132
01:28Synthetic Disvision of Polynomials
345
Synthetic division is an efficient algorithmic approach for dividing a polynomial by a linear binomial of the form x - c, where c is a real number. This method is helpful due to its streamlined process, which avoids the more cumbersome steps involved in the traditional long division of polynomials. It simplifies computation and serves as a practical tool for evaluating polynomials and identifying their factors.To perform synthetic division, one begins by listing the coefficients of the...
345
01:26Integration by Parts: Indefinite Integrals
493
Integration by parts is a fundamental technique in calculus for evaluating integrals involving the product of two functions. It is particularly useful when direct integration is not feasible. The method is based on the product rule for differentiation, which states that the derivative of a product equals the derivative of the first function times the second, plus the first function times the derivative of the second. By integrating this identity and rearranging terms, the integration by parts...
493