• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.273-283
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• 2001

We introduce sums and joins of T-fuzzy transformation semi-groups and investigate their algebraic structures.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.41-55
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• 1992

The characteristic free representation theory of the general linear group is one of the powerful tools in the study of invariant theory, algebraic geometry, and commutative algebra. Recently the study of such representations became a popular theme. In this paper we study the representation-theoretic structures of the symmetric algebra and the exterior algebra over a commutative ring with unity 1.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.211-221
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• 2007

In this paper, we define ${\bigwedge}$-structure, ${\bigvee}$-structure to generalize some lattices, and study the conditions that a lattice which has ${\bigwedge}$-structure or ${\bigvee}$-structure to be continuous or algebraic.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.2
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• pp.173-177
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• 2001

We introduce cascade products, wreath products, sums and joins of TL-finite state machines and investigate their algebraic structures. Also we study the relations with other products of TL-finite state machines.

• Journal for History of Mathematics
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• v.12 no.2
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• pp.151-158
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• 1999

In this paper, the concepts of semiprime $L$-fuzzy ideals and semiprimary $L$-fuzzy ideals of a $L$-fuzzy ring are introduced and some fundamental propositions proved. And we investigate the relation between fuzzy nil radical and semiprimary.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.05a
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• pp.25-28
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• 2001

We introduce sums and joins of fuzzy finite state machines and investigate their algebraic structures.

• Korean Journal of Logic
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• v.19 no.3
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• pp.437-461
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• 2016

This paper investigates weakening-free fuzzy logics with three weak forms of associativity (of multiplicative conjunction &). First, the wta-uninorm (based) logic $WA_tMUL$ and its two axiomatic extensions are introduced as weakening-free weakly associative fuzzy logics. The algebraic structures corresponding to the systems are then defined, and algebraic completeness results for them are provided. Next, standard completeness is established for $WA_tMUL$ and the two axiomatic extensions with an additional axiom using construction in the style of Jenei-Montagna.

• Korean Journal of Logic
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• v.17 no.2
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• pp.323-349
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• 2014

In this paper, we show that the standard completeness for the extension of UL with compensation-free reinforcement (cfr) $(({\phi}&{\psi}){\rightarrow}({\phi}{\wedge}{\psi})){\vee}(({\phi}{\vee}{\psi}){\rightarrow}({\phi}&{\psi}))$ can be established. More exactly, first, the compensation-freely reinforced uninorm logic $UL_{cfr}$ (the UL with (cfr)) is introduced. The algebraic structures of $UL_{cfr}$ are then defined, and its algebraic completeness is established. Next, standard completeness (i.e. completeness on [0, 1]) is established for $UL_{cfr}$ by using the method introduced in Yang (2009).

• Journal for History of Mathematics
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• v.28 no.6
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• pp.301-310
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• 2015

Since Jiuzhang Suanshu, the main tools in the theory of right triangles, known as Gougushu in East Asia were algebraic identities about three sides of a right triangle derived from the Pythagorean theorem. Using tianyuanshu up to siyuanshu, Song-Yuan mathematicians could skip over those identities in the theory. Chinese Mathematics in the 17-18th centuries were mainly concerned with the identities along with the western geometrical proofs. Jeong Yag-yong (1762-1836), a well known Joseon scholar and writer of the school of Silhak, noticed that those identities can be derived through algebra and then wrote Gugo Wonlyu (勾股源流) in the early 19th century. We show that Jeong reveals the algebraic structure of polynomials with the three indeterminates in the book along with their order structure. Although the title refers to right triangles, it is the first pure algebra book in Joseon mathematics, if not in East Asia.

• Korean Journal of Logic
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• v.23 no.1
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• pp.1-23
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• 2020

This paper deals with mianorm-based logics with right and left n-potency axioms and their fixpointed involutive extensions. For this, first, right and left n-potent logic systems based on mianorms, their corresponding algebraic structures, and their algebraic completeness results are discussed. Next, completeness with respect to algebras whose lattice reduct is [0, 1], known as standard completeness, is established for these systems via Yang's construction in the style of Jenei-Montagna. Finally, further standard completeness results are introduced for their fixpointed involutive extensions.