What do we refer to when we say algebraic structure?
Clash Royale CLAN TAG#URR8PPP
up vote
2
down vote
favorite
A set of all the operations on set $A$ is called an algebraic structure on set $A$?
Can anybody explain this statement to me.
What I understand from this is that, consider a set $mathbbN $ then,
Algebraic structure on set $mathbbN$ is the collection of all operators on $mathbbN$ meaning,
Algebraic Structure $= +, times, cdots $?
I watched a couple of videos on YouTube about algebraic structure. Some of them seem to give some other different definitions of Algebraic Structures.
Can anyone explain what does it "precisely" refer to? The operator? Set of operators? The set $A$ itself?
abstract-algebra
asked Aug 20 at 13:21
William
885314
add a comment |Â
up vote
2
down vote
favorite
A set of all the operations on set $A$ is called an algebraic structure on set $A$?
Can anybody explain this statement to me.
What I understand from this is that, consider a set $mathbbN $ then,
Algebraic structure on set $mathbbN$ is the collection of all operators on $mathbbN$ meaning,
Algebraic Structure $= +, times, cdots $?
I watched a couple of videos on YouTube about algebraic structure. Some of them seem to give some other different definitions of Algebraic Structures.
Can anyone explain what does it "precisely" refer to? The operator? Set of operators? The set $A$ itself?
abstract-algebra
asked Aug 20 at 13:21
William
885314
1
This has been answered here already. For some links, see here.
– Dietrich Burde
Aug 20 at 13:29
1
@DietrichBurde idk it's about why algebraic structures are used. My question is what exactly are Algebraic Structures?
– William
Aug 20 at 13:37
This is also answered there. In particular, it says "a class of algebraic structures is called a variety of algebras if it can be defined using only equations (like $xcdot (ycdot z) = (xcdot y) cdot z$). Examples of varieties are groups, rings, modules, boolean algebras... Varieties are the core topic of study in the field of universal algebra". Did you have a look at other related links there?
– Dietrich Burde
Aug 20 at 13:41
So one possible answer to your question (see title) "What do we refer to when we say algebraic structure?" is varieties of algebras.
– Dietrich Burde
Aug 20 at 13:44
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
A set of all the operations on set $A$ is called an algebraic structure on set $A$?
Can anybody explain this statement to me.
What I understand from this is that, consider a set $mathbbN $ then,
Algebraic structure on set $mathbbN$ is the collection of all operators on $mathbbN$ meaning,
Algebraic Structure $= +, times, cdots $?
I watched a couple of videos on YouTube about algebraic structure. Some of them seem to give some other different definitions of Algebraic Structures.
Can anyone explain what does it "precisely" refer to? The operator? Set of operators? The set $A$ itself?
abstract-algebra
asked Aug 20 at 13:21
William
885314
A set of all the operations on set $A$ is called an algebraic structure on set $A$?
Can anybody explain this statement to me.
What I understand from this is that, consider a set $mathbbN $ then,
Algebraic structure on set $mathbbN$ is the collection of all operators on $mathbbN$ meaning,
Algebraic Structure $= +, times, cdots $?
I watched a couple of videos on YouTube about algebraic structure. Some of them seem to give some other different definitions of Algebraic Structures.
Can anyone explain what does it "precisely" refer to? The operator? Set of operators? The set $A$ itself?
abstract-algebra
asked Aug 20 at 13:21
William
885314
edited Aug 21 at 12:00
asked Aug 20 at 13:21
William
885314
asked Aug 20 at 13:21
William
885314
asked Aug 20 at 13:21
William
885314
885314
1
This has been answered here already. For some links, see here.
– Dietrich Burde
Aug 20 at 13:29
1
@DietrichBurde idk it's about why algebraic structures are used. My question is what exactly are Algebraic Structures?
– William
Aug 20 at 13:37
This is also answered there. In particular, it says "a class of algebraic structures is called a variety of algebras if it can be defined using only equations (like $xcdot (ycdot z) = (xcdot y) cdot z$). Examples of varieties are groups, rings, modules, boolean algebras... Varieties are the core topic of study in the field of universal algebra". Did you have a look at other related links there?
– Dietrich Burde
Aug 20 at 13:41
So one possible answer to your question (see title) "What do we refer to when we say algebraic structure?" is varieties of algebras.
– Dietrich Burde
Aug 20 at 13:44
add a comment |Â
1
This has been answered here already. For some links, see here.
– Dietrich Burde
Aug 20 at 13:29
1
@DietrichBurde idk it's about why algebraic structures are used. My question is what exactly are Algebraic Structures?
– William
Aug 20 at 13:37
This is also answered there. In particular, it says "a class of algebraic structures is called a variety of algebras if it can be defined using only equations (like $xcdot (ycdot z) = (xcdot y) cdot z$). Examples of varieties are groups, rings, modules, boolean algebras... Varieties are the core topic of study in the field of universal algebra". Did you have a look at other related links there?
– Dietrich Burde
Aug 20 at 13:41
So one possible answer to your question (see title) "What do we refer to when we say algebraic structure?" is varieties of algebras.
– Dietrich Burde
Aug 20 at 13:44
1
1
This has been answered here already. For some links, see here.
– Dietrich Burde
Aug 20 at 13:29
This has been answered here already. For some links, see here.
– Dietrich Burde
Aug 20 at 13:29
1
1
@DietrichBurde idk it's about why algebraic structures are used. My question is what exactly are Algebraic Structures?
– William
Aug 20 at 13:37
@DietrichBurde idk it's about why algebraic structures are used. My question is what exactly are Algebraic Structures?
– William
Aug 20 at 13:37
This is also answered there. In particular, it says "a class of algebraic structures is called a variety of algebras if it can be defined using only equations (like $xcdot (ycdot z) = (xcdot y) cdot z$). Examples of varieties are groups, rings, modules, boolean algebras... Varieties are the core topic of study in the field of universal algebra". Did you have a look at other related links there?
– Dietrich Burde
Aug 20 at 13:41
This is also answered there. In particular, it says "a class of algebraic structures is called a variety of algebras if it can be defined using only equations (like $xcdot (ycdot z) = (xcdot y) cdot z$). Examples of varieties are groups, rings, modules, boolean algebras... Varieties are the core topic of study in the field of universal algebra". Did you have a look at other related links there?
– Dietrich Burde
Aug 20 at 13:41
So one possible answer to your question (see title) "What do we refer to when we say algebraic structure?" is varieties of algebras.
– Dietrich Burde
Aug 20 at 13:44
So one possible answer to your question (see title) "What do we refer to when we say algebraic structure?" is varieties of algebras.
– Dietrich Burde
Aug 20 at 13:44
add a comment |Â
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2888784%2fwhat-do-we-refer-to-when-we-say-algebraic-structure%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
1
This has been answered here already. For some links, see here.
– Dietrich Burde
Aug 20 at 13:29
1
@DietrichBurde idk it's about why algebraic structures are used. My question is what exactly are Algebraic Structures?
– William
Aug 20 at 13:37
This is also answered there. In particular, it says "a class of algebraic structures is called a variety of algebras if it can be defined using only equations (like $xcdot (ycdot z) = (xcdot y) cdot z$). Examples of varieties are groups, rings, modules, boolean algebras... Varieties are the core topic of study in the field of universal algebra". Did you have a look at other related links there?
– Dietrich Burde
Aug 20 at 13:41
So one possible answer to your question (see title) "What do we refer to when we say algebraic structure?" is varieties of algebras.
– Dietrich Burde
Aug 20 at 13:44